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  • 351.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Inverse Problems in Analytic Interpolation for Robust Control and Spectral Estimation2008Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis is divided into two parts. The first part deals with theNevanlinna-Pick interpolation problem, a problem which occursnaturally in several applications such as robust control, signalprocessing and circuit theory. We consider the problem of shaping andapproximating solutions to the Nevanlinna-Pick problem in a systematicway. In the second part, we study distance measures between powerspectra for spectral estimation. We postulate a situation where wewant to quantify robustness based on a finite set of covariances, andthis leads naturally to considering the weak*-topology. Severalweak*-continuous metrics are proposed and studied in this context.In the first paper we consider the correspondence between weighted entropyfunctionals and minimizing interpolants in order to find appropriateinterpolants for, e.g., control synthesis. There are two basic issues that weaddress: we first characterize admissible shapes of minimizers bystudying the corresponding inverse problem, and then we developeffective ways of shaping minimizers via suitable choices of weights.These results are used in order to systematize feedback controlsynthesis to obtain frequency dependent robustness bounds with aconstraint on the controller degree.The second paper studies contractive interpolants obtained as minimizersof a weighted entropy functional and analyzes the role of weights andinterpolation conditions as design parameters for shaping theinterpolants. We first show that, if, for a sequence of interpolants,the values of the corresponding entropy gains converge to theoptimum, then the interpolants converge in H_2, but not necessarily inH-infinity. This result is then used to describe the asymptoticbehaviour of the interpolant as an interpolation point approaches theboundary of the domain of analyticity.A quite comprehensive theory of analytic interpolation with degreeconstraint, dealing with rational analytic interpolants with an apriori bound, has been developed in recent years. In the third paper,we consider the limit case when this bound is removed, and only stableinterpolants with a prescribed maximum degree are sought. This leadsto weighted H_2 minimization, where the interpolants areparameterized by the weights. The inverse problem of determining theweight given a desired interpolant profile is considered, and arational approximation procedure based on the theory is proposed. Thisprovides a tool for tuning the solution for attaining designspecifications. The purpose of the fourth paper is to study the topology and develop metricsthat allow for localization of power spectra, based on second-orderstatistics. We show that the appropriate topology is theweak*-topology and give several examples on how to construct suchmetrics. This allows us to quantify uncertainty of spectra in anatural way and to calculate a priori bounds on spectral uncertainty,based on second-order statistics. Finally, we study identification ofspectral densities and relate this to the trade-off between resolutionand variance of spectral estimates.In the fifth paper, we present an axiomatic framework for seekingdistances between power spectra. The axioms requirethat the sought metric respects the effects of additive andmultiplicative noise in reducing our ability to discriminate spectra.They also require continuity of statistical quantities withrespect to perturbations measured in the metric. We then present aparticular metric which abides by these requirements. The metric isbased on the Monge-Kantorovich transportation problem and iscontrasted to an earlier Riemannian metric based on theminimum-variance prediction geometry of the underlying time-series. Itis also being compared with the more traditional Itakura-Saitodistance measure, as well as the aforementioned prediction metric, ontwo representative examples.

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  • 352.
    Enqvist, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Minimal Itakura-Saito distance and Covariance interpolation2008In: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, p. 137-142Conference paper (Refereed)
    Abstract [en]

    Identification of power spectral densities rely on measured second order statistics such as, e.g. covariance estimates. In the family of power spectra consistent with such an estimate a representative spectra is singled out; examples of such choices are the Maximum entropy spectrum and the Correlogram. Here, we choose a prior spectral density to represent a priori information, and the spectrum closest to the prior in the Itakura-Saito distance is selected. It is known that this can be seen as the limit case when the cross-entropy principle is applied to a gaussian process. This work provides a quantitative measure of how close a finite covariance sequence is to a spectral density in the Itakura-Saito distance. It is given by a convex optimization problem and by considering its dual the structure of the optimal spectrum is obtained. Furthermore, it is shown that strong duality holds and that a covariance matching coercive spectral density always exists. The methods presented here provides tools for discrimination between power spectrum, identification of power spectrum, and for incorporating given data in this process.

  • 353. Ni, W.
    et al.
    Cheng, D.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Minimum dwell time for stability and stabilization of switched linear systems2008In: Proc. World Congr. Intelligent Control Autom. WCICA, 2008, p. 4103-4108Conference paper (Refereed)
    Abstract [en]

    In this paper, the problem of minimum dwell time for the stability and stabilization of switched linear systems is considered. First, using the method of multiple Lyapunov functions, we obtain an estimate for the minimum dwell time(MDT), which assures the exponential stability of switched linear systems. Using the stability result obtained for free system, we then investigate the problem of MDT for stabilization of switched linear control system subject to input constraints. Under certain conditions the exponential stabilization can be achieved by using controls with restricted amplitudes as long as the switching laws satisfy the MDT time requirement. An illustrative example is presented to show the validity of the results.

  • 354.
    Anisi, David A.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Ögren, Petter
    Minimum time multi-UGV surveillance2008In: OPTIMIZATION AND COOPERATIVE CONTROL STRATEGIES / [ed] Hirsch MJ; Commander CW; Pardalos PM; Murphey R, Berlin: Springer Verlag , 2008, p. 31-45Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of concurrent task- and path planning for a number of  surveillance Unmanned Ground Vehicles (UGVs) such that a user defined area of interest is covered by the UGVs' sensors in minimum time. We first formulate the problem, and show that it is in fact  a generalization of the Multiple Traveling Salesmen Problem (MTSP), which is known to be NP-hard. We then propose a solution that decomposes the problem into three subproblems. The first is to find a maximal convex covering of the search area. Most results on static coverage  use disjoint partitions of the search area, e.g. triangulation, to convert the continuous sensor positioning problem into a  discrete one. However, by a simple example, we show that a highly overlapping set of maximal convex sets is better suited for  minimum time coverage. The second subproblem is a combinatorial assignment and ordering of the sets in the cover.  Since Tabu search algorithms are known to perform well on various routing problems,  we use it as a part of our proposed solution. Finally, the third subproblem utilizes a particular shortest path sub-routine in order to find the vehicle paths, and calculate the overall objective function used in the Tabu search. The proposed algorithm is illustrated by a number of simulation examples.

  • 355.
    Fanizza, Giovanna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Modeling and Model Reduction by Analytic Interpolation and Optimization2008Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    This thesis consists of six papers. The main topic of all these papers is modeling a class of linear time-invariant systems. The system class is parameterized in the context of interpolation theory with a degree constraint. In the papers included in the thesis, this parameterization is the key tool for the design of dynamical system models in fields such as spectral estimation and model reduction. A problem in spectral estimation amounts to estimating a spectral density function that captures characteristics of the stochastic process, such as covariance, cepstrum, Markov parameters and the frequency response of the process. A  model reduction problem consists in finding a small order system which replaces the original one so that the behavior of both systems is similar in an appropriately defined sense.  In Paper A a new spectral estimation technique based on the rational covariance extension theory is proposed. The novelty of this approach is in the design of a spectral density that optimally matches covariances and approximates the frequency response of a given process simultaneously.In Paper B  a model reduction problem is considered. In the literature there are several methods to perform model reduction. Our attention is focused on methods which preserve, in the model reduction phase, the stability and the positive real properties of the original system. A reduced-order model is computed employing the analytic interpolation theory with a degree constraint. We observe that in this theory there is a freedom in the placement of the spectral zeros and interpolation points. This freedom can be utilized for the computation of a rational positive real function of low degree which approximates the best a given system. A problem left open in Paper B is how to select spectral zeros and interpolation points in a systematic way in order to obtain the best approximation of a given system. This problem is the main topic in Paper C. Here, the problem is investigated in the analytic interpolation context and spectral zeros and interpolation points are obtained as solution of a optimization problem.In Paper D, the problem of modeling a floating body by a positive real function is investigated. The main focus is  on modeling the radiation forces and moment. The radiation forces are described as the forces that make a floating body oscillate in calm water. These forces are passive and usually they are modeled with system of high degree. Thus, for efficient computer simulation it is necessary to obtain a low order system which approximates the original one. In this paper, the procedure developed in Paper C is employed. Thus, this paper demonstrates the usefulness of the methodology described in Paper C for a real world application.In Paper E, an algorithm to compute the steady-state solution of a discrete-type Riccati equation, the Covariance Extension Equation, is considered. The algorithm is based on a homotopy continuation method with predictor-corrector steps. Although this approach does not seem to offer particular advantage to previous solvers, it provides insights into issues such as positive degree and model reduction, since the rank of the solution of the covariance extension problem coincides with the degree of the shaping filter. In Paper F a new algorithm for the computation of the analytic interpolant of a bounded degree is proposed. It applies to the class of non-strictly positive real interpolants and it is capable of treating the case with boundary spectral zeros. Thus, in Paper~F, we deal with a class of interpolation problems which could not be treated by the optimization-based algorithm proposed by Byrnes, Georgiou and Lindquist. The new procedure computes interpolants by solving a system of nonlinear equations. The solution of the system of nonlinear equations is obtained by a homotopy continuation method.

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  • 356.
    Branke, Jürgen
    et al.
    University of Karlsruhe, Institute AIFB, Germany.
    Deb, KalyanmoyMiettinen, KaisaKTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.Slowinski, RomanPoznan University of Technology, Institute of Computing Science.
    Multiobjective Optimization: Interactive and Evolutionary Approaches2008Collection (editor) (Refereed)
  • 357. Gustavi, Tove
    et al.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Observer-Based Leader-Following Formation Control Using Onboard Sensor Information2008In: IEEE Transactions on robotics, ISSN 1552-3098, E-ISSN 1941-0468, ISSN 1552-3098, Vol. 24, no 6, p. 1457-1462Article in journal (Refereed)
    Abstract [en]

    In this paper, leader-following formation control for mobile multiagent systems with limited sensor information is studied. The control algorithms developed require information available from onboard sensors only, and in particular, the measurement of the leader (neighbor) speed is not needed. Instead, an observer Is designed for the estimation of this speed, With the proposed control algorithms as building blocks, many complex formations can be obtained.

  • 358.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On Methods for Discrete Topology Optimization of Continuum Structures2008Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    This thesis consists of an introduction and seven appended papers. The purpose of the introduction is to give an overview of the field of topology optimization of discretized load carrying continuum structures. It is assumed that the design domain has been discretized by the finite element method and that the design variable vector is a binary vector indicating presence or absence of material in the various finite elements. Common to all papers is the incorporation of von Mises stresses in the problem formulations.

    In the first paper the design variables are binary but it is assumed that the void structure can actually take some load. This is equivalent to adding a small positive value, epsilon, to all design variables, both those that are void and those that are filled with material. With this small positive lower bound the stiffness matrix becomes positive definite for all designs. If only one element is changed (from material to void or from void to material) the new global stiffness matrix is just a low rank modification of the old one and thus the Sherman-Morrison-Woodbury formula can be used to compute the displacements in the neighbouring designs efficiently. These efficient sensitivity calculations can then be applied in the context of a neighbourhood search method. Since the computed displacements are exact in the 1-neighbourhood (when one design variable is changed) the neighbourhood search method will find a local optimum with respect to the 1-neighbourhood.

    The second paper presents globally optimal zero-one solutions to some small scale topology optimization problems defined on discretized continuum design domains. The idea is that these solutions can be used as benchmarks when testing new algorithms for finding pure zero-one solutions to topology optimization problems.

    In the third paper the results from the first paper are extended to include also the case where there is no epsilon>0. In this case the stiffness matrix will no longer be positive definite which means that the Sherman-Morrison-Woodbury formula can no longer be applied. The changing of one or two binary design variables to their opposite binary values will still result in a low rank change, but the size of the reduced stiffness matrix will change with the design. It turns out, however, that it is possible to compute the effect of these low rank changes efficiently also without the positive lower bound. These efficient sensitivity calculations can then be used in the framework of a neighbourhood search method. In this case the complete 1-neighbourhood and a subset of the 2-neighbourhood is investigated in the search for a locally optimal solution.

    In the fourth paper the sensitivity calculations developed in the third paper are used to generate first and partial second order approximations of the nonlinear functions usually present in topology optimization problems. These approximations are then used to generate subproblems in two different sequential integer programming methods (SLIP and SQIP, respectively). Both these methods generate a sequence of iteration points that can be proven to converge to a local optimum with respect to the 1-neighbourhood. The methods are tested on some different topology optimization problems.

    The fifth paper demonstrates that the SLIP method developed in the previous paper can be applied also to the mechanism design problem with stress constraints. In order to generate the subproblems in a fast way small displacements are assumed, which implies that the efficient sensitivity calculations derived in the third paper can be used. The numerical results indicate that the method can be used to lower the stresses and still get a functional mechanism.

    In the sixth paper the SLIP method developed in the fourth paper is used as a post processor to obtain locally optimal zero-one solutions starting from a rounded solution to the corresponding continuous problem. The numerical results indicate that the method can perform well as a post processor.

    The seventh paper is a theoretical paper that investigates the validity of the commonly used positive lower bound epsilon on the design variables when stating and solving topology optimization problems defined on discretized load carrying continuum structures. The main result presented here is that an optimal "epsilon-1" solution to an "epsilon-perturbed" discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to zero-one, to the corresponding "unperturbed" discrete problem. This holds if the constraints in the perturbed problem are carefully defined and epsilon>0 is sufficiently small.

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  • 359.
    Jönsson, Ulf
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Cantoni, M.
    Kao, C. -Y
    On Structured Robustness Analysis for Feedback Interconnections of Unstable Systems2008In: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, p. 351-356Conference paper (Refereed)
    Abstract [en]

    The purpose of this paper is to broaden the scope of integral-quadratic-constraint based structured robustness analysis in a way that accommodates feedback interconnections of unstable linear time-invariant systems. This is achieved by exploring the use of Vinnicombe's nu-gap metric as a measure of distance. Various standard robustness analysis problems are revisited within the context of the main result.

  • 360.
    Hu, Jiangping
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Optimal Target Trajectory Estimation and Filtering Using Networked Sensors2008In: PROCEEDINGS OF THE 27TH CHINESE CONTROL CONFERENCE, VOL 7 / [ed] Cheng, D., HAIDIAN QU DISTRICT: BEIJING UNIV AERONAUTICS & ASTRONAUTICS PRESS , 2008, p. 540-545Conference paper (Refereed)
    Abstract [en]

    Target tracking using distributed sensor network is in general a challenging problem because it always needs to deal with real-time processing of noisy information. In this paper the problem of using nonlinear sensors such as distance and direction sensors for estimating a moving target is studied. The problem is formulated as a prudent design of nonlinear filters fora linear system subject to noisy nonlinear measurements and partially unknown input, which is generated by an exogenous system. In the worst case where the input is completely unknown, the exogenous dynamics is reduced to the random walk model. It can be shown that the nonlinear filter will have optimal convergence if the number of the sensors are large enough and the convergence rate will be highly improved if the sensors are deployed appropriately. This actually raises an interesting issue on active sensing: how to optimally move the sensors if they are considered as mobile multi-agent systems? Finally, a simulation example is given to illustrate and validate the construction of our filter.

  • 361.
    Hu, Jiangping
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimal target trajectory estimation and filtering using networked sensors2008In: Journal of Systems Science and Complexity, ISSN 1009-6124, E-ISSN 1559-7067, Vol. 21, no 3, p. 325-336Article in journal (Refereed)
    Abstract [en]

    Target tracking using distributed sensor network is in general a challenging problem because it always needs to deal with real-time processing of noisy information. In this paper the problem of using nonlinear sensors such as distance and direction sensors for estimating a moving target is studied. The problem is formulated as a prudent design of nonlinear filters for a linear system subject to noisy nonlinear measurements and partially unknown input, which is generated by an exogenous system. In the worst case where the input is completely unknown, the exogenous dynamics is reduced to the random walk model. It can be shown that the nonlinear filter will have optimal convergence if the number of the sensors are large enough and the convergence rate will be highly improved if the sensors are deployed appropriately. This actually raises an interesting issue on active sensing: how to optimally move the sensors if they are considered as mobile multi-agent systems? Finally, a simulation example is given to illustrate and validate the construction of our filter.

  • 362.
    Fanizza, Giovanna
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Passive system with degree bound designed by analytic interpolation2008Article in journal (Other academic)
  • 363.
    Kuroiwa, Yohei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sensitivity Shaping under Degree Constraint: Nevanlinna-Pick Interpolation for Multivarible and Time-Delay Systems2008Licentiate thesis, comprehensive summary (Other scientific)
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  • 364.
    Hu, Xiaoming
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hong, Yiguang
    Chinese Acad Sci, Beijing, Peoples R China..
    Bushnell, Linda
    Univ Washington, Seattle, WA 98195 USA..
    Special issue on "collective behavior and control of multi-agent systems"2008In: Asian journal of control, ISSN 1561-8625, E-ISSN 1561-8625, Vol. 10, no 2, p. 129-130Article in journal (Other academic)
  • 365.
    Karlsson, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Stability-preserving rational approximation subject to interpolation constraints2008In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, no 7, p. 1724-1730Article in journal (Refereed)
    Abstract [en]

    A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational analytic interpolants with an a priori bound, has been developed in recent years. In this paper, we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H-2 minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded analytic interpolants.

  • 366. Cheng, D.
    et al.
    Wang, J.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Stabilization of switched linear systems via LaSalle's invariance principle2008Conference paper (Refereed)
    Abstract [en]

    This paper considers the stability of switched linear systems. Assume a common weak quadratic Lyapunov function exists and the switches satisfy certain ergodic property, we investigate two extensions of LaSalle's invariance principle. Unlike most existing results, the systems we investigated may have switching modes, which are not asymptotically stable. An application to the consensus of multi-agent systems is presented.

  • 367. Iannelli, Luigi
    et al.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Vasca, Francesco
    Subtleties in the averaging of a class of hybrid systems with applications to power converters2008In: Control Engineering Practice, ISSN 0967-0661, E-ISSN 1873-6939, Vol. 16, no 8, p. 961-975Article in journal (Refereed)
    Abstract [en]

    High-frequency dither signals are commonly used to implement modulation schemes in power electronics converters. These systems represent an interesting class of hybrid systems with external excitation. They have a rich dynamical behavior, which cannot be easily understood intuitively. Despite the common use of averaging techniques in power electronics, it was only recently proved that a dithered hybrid system can be approximated by an averaged system under certain conditions on the dither signal. Averaging and averaged models for various types of power converters are analyzed in the paper. It is shown that the averaged nonlinearity depends on the dither shape and that dither signals with Lipschitz-continuous averaged nonlinearities can be used to adapt the equivalent gain of power converters. Practical stability of the original dithered system can be inferred by analyzing a simpler averaged system. The main contribution of the paper is to show that the averaged and the dithered systems may have drastically different behavior if the assumptions of the recently developed averaging theory for dithered hybrid systems are violated. Several practical experiments and simulation examples of power electronics converters are discussed. They indicate that the conditions on the dither signal imposed by the averaging theory are rather tight.

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    dither_cep08
  • 368.
    Karlsson, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Takyar, Mir Shahrouz
    Georgiou, Tryphon T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Transport metrics for power spectra2008In: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, p. 143-148Conference paper (Refereed)
    Abstract [en]

    We present a family of metrics for power spectra based on the Monge-Kantorivic transportation distances. These metrics are constructed so that distances reduce with additive and multiplicative noise, reflecting the intuition that noise typically reduces our ability to discriminate spectra. In addition, perturbations measured in these metrics are continuous with respect to the statistics of the underlying time series. A general framework for constructing such metrics is put forth and these are contrasted with an earlier Riemannian metric which is based on prediction theory and the relevant geometry of the underlying time-series.

  • 369.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Using the sequential linear integer programming method as a post-processor for stress-constrained topology optimization problems2008In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 76, no 10, p. 1544-1567Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of load-carrying structures defined on discretized continuum design domains. In particular, the mininium compliance problem with stress constraints is considered. The finite element method is used to discretize the design domain into n finite elements and the design of a certain structure is represented by an n-dimensional binary design variable vector. In order to solve the problems, the binary constraints on the design variables are initially relaxed and the problems are solved with both the method of moving asymptotes and the sparse non-linear optimizer solvers for continuous optimization in order to compare the two solvers. By solving a sequence of problems with a sequentially lower limit on the amount of grey allowed, designs that are close to 'black-and-white' are obtained. In order to get locally optimal solutions that are purely {0, 1}(n). a sequential linear integer programming method is applied as a post-processor. Numerical results are presented for some different test problems.

  • 370.
    Carlsson, Fredrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Utilizing Problem Structure in Optimization of Radiation Therapy2008Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    In this thesis, optimization approaches for intensity-modulated radiation therapy are developed and evaluated with focus on numerical efficiency and treatment delivery aspects. The first two papers deal with strategies for solving fluence map optimization problems efficiently while avoiding solutions with jagged fluence profiles. The last two papers concern optimization of step-and-shoot parameters with emphasis on generating treatment plans that can be delivered efficiently and accurately. In the first paper, the problem dimension of a fluence map optimization problem is reduced through a spectral decomposition of the Hessian of the objective function. The weights of the eigenvectors corresponding to the p largest eigenvalues are introduced as optimization variables, and the impact on the solution of varying p is studied. Including only a few eigenvector weights results in faster initial decrease of the objective value, but with an inferior solution, compared to optimization of the bixel weights. An approach combining eigenvector weights and bixel weights produces improved solutions, but at the expense of the pre-computational time for the spectral decomposition. So-called iterative regularization is performed on fluence map optimization problems in the second paper. The idea is to find regular solutions by utilizing an optimization method that is able to find near-optimal solutions with non-jagged fluence profiles in few iterations. The suitability of a quasi-Newton sequential quadratic programming method is demonstrated by comparing the treatment quality of deliverable step-and-shoot plans, generated through leaf sequencing with a fixed number of segments, for different number of bixel-weight iterations. A conclusion is that over-optimization of the fluence map optimization problem prior to leaf sequencing should be avoided. An approach for dynamically generating multileaf collimator segments using a column generation approach combined with optimization of segment shapes and weights is presented in the third paper. Numerical results demonstrate that the adjustment of leaf positions improves the plan quality and that satisfactory treatment plans are found with few segments. The method provides a tool for exploring the trade-off between plan quality and treatment complexity by generating a sequence of deliverable plans of increasing quality. The final paper is devoted to understanding the ability of the column generation approach in the third paper to find near-optimal solutions with very few columns compared to the problem dimension. The impact of different restrictions on the generated columns is studied, both in terms of numerical behaviour and convergence properties. A bound on the two-norm of the columns results in the conjugate-gradient method. Numerical results indicate that the appealing properties of the conjugate-gradient method on ill-conditioned problems are inherited in the column generation approach of the third paper.

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  • 371.
    Lindquist, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Georgiou, Tryphon
    Weight selection for gap robustness with degree-constrained controllers2008In: Proc. 47th IEEE Conference on Decision and Control, 2008, p. 4127-4134Conference paper (Refereed)
    Abstract [en]

    In modern robust control, control synthesis may be cast as an interpolation problem where the interpolant relates to robustness and performance criteria. In particular,robustness in the gap fits into this framework and the magnitude of the corresponding interpolant dictate the robustness to perturbations of the plant as a function of frequency. In this paper we consider the correspondence between weighted entropy functionals and minimizing interpolants in order to find appropriate interpolants for e.g. control synthesis. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. These results are used in order to systematize feedback control synthesis to obtain frequency dependentrobustness bounds with a constraint on the controller degree. 

  • 372.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung-Yao
    Fujioka, Hisaya
    A Popov criterion for networked systems2007In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 56, no 9-10, p. 603-610Article in journal (Refereed)
    Abstract [en]

    We consider robustness analysis of heterogeneous and homogeneous networked systems based on integral quadratic constraints (IQCs). First, we show how the analysis decomposes into lower dimensional problems if the interconnection structure is exploited. This generally leads to a significant reduction of the computational complexity. Secondly, by considering a set of IQCs that characterizes the eigenvalues of the interconnection matrices of symmetrically networked systems, we derive a Popov-like criterion for such systems. In particular, when the nodes of the networked system are single-input-single-output linear time-invariant operators, the criterion can be illustrated using a generalized Popov plot. In such cases. the Popov criterion is also a necessary condition in the sense that if the criterion is violated then a destabilizing network with the specified eigenvalue distribution can be constructed.

  • 373.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A time-periodic sector condition for limit cycle robustness2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 1513-1519Conference paper (Refereed)
    Abstract [en]

    Existence and robustness of periodic oscillations in autonomous feedback systems are considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude band range. The quadratic constraint is generated as a time-periodic sector condition that characterizes the nonlinearity along a nominal periodic solution. The main analysis condition is formulated as an operator inequality involving the nominal dynamics and the sector constraint. This is an infinite dimensional robustness test that must be truncated to be verified numerically. We discuss two possible ways of performing the analysis.

  • 374.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Martin, Clyde
    Approximation with the output of linear control systems2007In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 329, no 2, p. 798-821Article in journal (Refereed)
    Abstract [en]

    In this paper we give a new proof that for controllable and observable linear systems every L-2[0, T] function can be approximated in the L-2[0, T] sense with an output function generated by an L-2[0, T] input function. We also give a new characterization of how continuous functions on [0, T] are uniformly approximated by an output generated by a continuous input function. The relative degree of the transfer function of the system determines those functions that can be approximated. We further show that if the initial data is allowed to vary then every continuous function is uniformly approximated by outputs generated by continuous functions.

  • 375.
    Enqvist, Per
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Avventi, Enrico
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Approximative covariance interpolation with a quadratic penalty2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 4489-4494Conference paper (Refereed)
    Abstract [en]

    Given output data of a stationary stochastic process estimates of the covariances parameters can be obtained. These estimates can be used to determine ARMA models to approximatly fit the data by matching the covariances exactly. However, the estimates of the covariances may contain large errors, especially if they are determined from short data sequences, and thus it makes sense to match the covariances only in an approximative way. Here we consider a convex method for solving an approximative covariance interpolation problem while maximizing the entropy and penalize the quadratic deviation from the nominal covariances.

  • 376. Kao, C. -Y
    et al.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fujioka, H.
    Characterization of robust stability of a class of interconnected systems2007In: American Control Conference, 2007. ACC '07, 2007, p. 784-789Conference paper (Refereed)
    Abstract [en]

    We consider robust stability analysis of a class of spatially interconnected systems. The individual subsystems may be different but they are assumed to share some properties that can be characterized by an integral quadratic constraint. The main contribution of the paper is to show that, for the case where the network interconnection matrix is normal, (robust) stability verification can be simplified to a simple problem of checking the location of the eigenvalues of the interconnection matrix. Most interestingly, we also identify a class of networks for which this characterization on eigenvalues is necessary and sufficient for robust stability.

  • 377.
    Karasalo, Maja
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Martin, Clyde R.
    Contour reconstruction and matching using recursive smoothing splines2007In: MODELING, ESTIMATION AND CONTROL: FESTSCHRIFT IN HONOR OF GIORGIO PICCI ON THE OCCASION OF THE SIXTY-FIFTH BIRTHDAY / [ed] Chiuso, A; Ferrante, A; Pinzoni, S, BERLIN: SPRINGER-VERLAG BERLIN , 2007, Vol. 364, p. 193-206Conference paper (Refereed)
    Abstract [en]

    In this paper a recursive smoothing spline approach is used for reconstructing a closed contour. Periodic splines are generated through minimizing a cost function subject to constraints imposed by a linear control system. The filtering effect of the smoothing splines allows for usage of noisy sensor data. An important feature of the method is that several data sets for the same closed contour can be processed recursively so that the accuracy can be improved meanwhile the current mapping can be used for planning the path for the data-collecting robot.

  • 378.
    Piccolo, Giacomo
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Karasalo, Maja
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Kragic, Danica
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Contour reconstruction using recursive smoothing splines experimental validation2007In: IEEE International Conference on Intelligent Robots and Systems: Vols 1-9, 2007, p. 2077-2082Conference paper (Refereed)
    Abstract [en]

    In this paper, a recursive smoothing spline approach for contour reconstruction is studied and evaluated. Periodic smoothing splines are used by a robot to approximate the contour of encountered obstacles in the environment. The splines are generated through minimizing a cost function subject to constraints imposed by a linear control system and accuracy is improved iteratively using a recursive spline algorithm. The filtering effect of the smoothing splines allows for usage of noisy sensor data and the method is robust to odometry drift. Experimental evaluation is performed for contour reconstruction of three objects using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics.

  • 379.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic phasor analysis of pulse-modulated systems2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 3938-3945Conference paper (Refereed)
    Abstract [en]

    The paper considers stability analysis of a general class of pulse modulated systems in a phasor dynamic framework. The dynamic phasor model exploits the cyclic nature of the modulation functions by representing the system dynamics in terms of a Fourier series expansion defined over a moving time-window. The contribution of the paper is to show that a special type of periodic Lyapunov function can be used to analyze the system and that the analysis conditions become tractable for computation after truncation. The approach provides a trade-off between complexity and accuracy that includes standard state space averaged models as a special case.

  • 380.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fujioka, Hisaya
    KTH. Kyoto University, Japan.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung Yao
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Patino, D.
    Riedinger, P.
    Geyer, T.
    Beccuti, A.
    Papafotiou, G.
    Morari, M.
    Wernrud, A.
    Rantzer, A.
    Hybrid control techniques for switched-mode DC-DC converters part I: The step-down topology2007In: 2007 American Control Conference, IEEE , 2007, p. 5450-5457Conference paper (Refereed)
    Abstract [en]

    Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency synchronous step-down dc-dc converter. The specifications are defined such that good performance only can be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

  • 381. Beccuti, A. G.
    et al.
    Papafotiou, G.
    Morari, M.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fujioka, Hisaya
    KTH. Kyoto University, Japan.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung Yao
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. University of Melbourne, Australia.
    Wernrud, A.
    Rantzer, A.
    Bâja, M.
    Comierais, H.
    Buisson, J.
    Hybrid control techniques for switched-mode DC-DC converters part II: The step-up topology2007In: 2007 American Control Conference, Vols 1-13, 2007, p. 5464-5471Conference paper (Refereed)
    Abstract [en]

    Several recent techniques from hybrid and optimal control are evaluated on a power electronics benchmark problem. The benchmark involves a number of practically interesting operating scenarios for a fixed-frequency step-up dc-dc converter. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is respected during the design phase.

  • 382.
    Eskelinen, Petri
    et al.
    Helsinki School of Economics.
    Miettinen, Kaisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Klamroth, Kathrin
    Institute of Applied Mathematics, University of Erlangen Nuremberg.
    Hakanen, Jussi
    University of Jyväskylä.
    Interactive Learning-Oriented Decision Support Tool for Nonlinear Multiobjective Optimization: Pareto Navigator2007Report (Other academic)
    Abstract [en]

        We describe a new interactive learning-oriented method called Pareto navigatorfor nonlinear multiobjective optimization. In the method, first a polyhedral approx-imation of the Pareto optimal set is formed in the objective function space usinga relatively small set of Pareto optimal solutions representing the Pareto optimalset. Then the decision maker can navigate around the polyhedral approximationand direct the search for promising regions where the most preferred solution couldbe located. In this way, the decision maker can learn about the interdependenciesbetween the conflicting objectives and possibly adjust one’s preferences. Once aninteresting region has been identified, the polyhedral approximation can be mademore accurate in that region or the decision maker can ask for the closest counter-part in the actual Pareto optimal set. If desired, (s)he can continue with anotherinteractive method from the solution obtained. Pareto navigator can be seen as a nonlinear extension of the linear Pareto race method. Pareto navigator is computa-tionally efficient because most of the computations are performed in the polyhedralapproximation and for that reason function evaluations of the actual objective func-tions are not needed. Thus, the method is well suited especially for problems withcomputationally costly functions. Furthermore, thanks to the visualization tech-nique used, the method is applicable also for problems with three or more objectivefunctions, and in fact it is best suited for such problems. We illustrate the methodand the underlying ideas with an example.

  • 383. Byrnes, Christopher I.
    et al.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Interior point solutions of variational problems and global inverse function theorems2007In: International Journal of Robust and Nonlinear Control, ISSN 1049-8923, E-ISSN 1099-1239, Vol. 17, no 5-6, p. 463-481Article in journal (Refereed)
    Abstract [en]

    Variational problems and the solvability of certain nonlinear equations have a long and rich history beginning with calculus and extending through the calculus of variations. In this paper, we are interested in 'well-connected' pairs of such problems which are not necessarily related by critical point considerations. We also study constrained problems of the kind which arise in mathematical programming. We are also interested in interior minimizing points for the variational problem and in the well-posedness (in the sense of Hadamard) of solvability of the related systems of equations. We first prove a general result which implies the existence of interior points and which also leads to the development of certain generalization of the Hadamard-type global inverse function theorem, along the theme that uniqueness quite often implies existence. This result is illustrated by proving the non-existence of shock waves for certain initial data for the vector Burgers' equation. The global inverse function theorem is also illustrated by a derivation of the existence of positive definite solutions of matrix Riccati equations without first analysing the nonlinear matrix Riccati differential equation. The main results on the existence of solutions to geometrically constrained well-connected pairs are then presented and illustrated by a geometric analysis of the existence of interior points for linear programming problems.

  • 384.
    Forsgren, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Gill, Philip E.
    Griffin, Joshua D.
    Iterative solution of augmented systems arising in interior methods2007In: SIAM Journal on Optimization, ISSN 1052-6234, E-ISSN 1095-7189, Vol. 18, no 2, p. 666-690Article in journal (Refereed)
    Abstract [en]

    Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods de. ne a sequence of KKT equations that represent the symmetrized ( but indefinite) equations associated with Newton's method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dual variables and become increasingly ill- conditioned as the optimization proceeds. In this context, an iterative linear solver must not only handle the ill- conditioning but also detect the occurrence of KKT matrices with the wrong matrix inertia. A one- parameter family of equivalent linear equations is formulated that includes the KKT system as a special case. The discussion focuses on a particular system from this family, known as the " doubly augmented system," that is positive definite with respect to both the primal and dual variables. This property means that a standard preconditioned conjugate- gradient method involving both primal and dual variables will either terminate successfully or detect if the KKT matrix has the wrong inertia. Constraint preconditioning is a well- known technique for preconditioning the conjugate- gradient method on augmented systems. A family of constraint preconditioners is proposed that provably eliminates the inherent ill- conditioning in the augmented system. A considerable benefit of combining constraint preconditioning with the doubly augmented system is that the preconditioner need not be applied exactly. Two particular " active- set" constraint preconditioners are formulated that involve only a subset of the rows of the augmented system and thereby may be applied with considerably less work. Finally, some numerical experiments illustrate the numerical performance of the proposed preconditioners and highlight some theoretical properties of the preconditioned matrices.

  • 385.
    Fanizza, Giovanna
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Unneland, Kari
    Department of Engineering Cybernetics, Norwegian University of Science and Technology.
    Low order radiation forces by analytic interpolation with degree constraint2007In: Proceedings of the 46th IEEE conference on decision and control, 2007, p. 2405-2410Conference paper (Refereed)
    Abstract [en]

    The positive real modeling of a floating body is considered, whereas the main focus is on the radiation forces and moments. The radiation forces and moments describe the interaction of a floating body with the surrounding fluid. This type of mathematical model is of interest in among control and simulation of dynamical positioned vessels (i.e. ships and offshore platforms) and wave power plants. It has been proven that the radiation forces are passive, but very little attention have been drawn towards low order passive identification of these forces. Traditionally high order models have been obtained, and subsequently model order reduction have been applied to obtain low order models. Here, a direct approach for obtaining low order passive models using analytic interpolation with a degree constraint is applied. A case study involving a 3 degrees of freedom surface vessel is shown to illustrate the features of the proposed approach.

  • 386. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    LQ optimal control for a class of pulse width modulated systems2007In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, no 6, p. 1009-1020Article in journal (Refereed)
    Abstract [en]

    We consider linear quadratic optimal control for a class of pulse width modulated systems. The problem is motivated from a practical application-digital control of switching power converters. The control synthesis problem is posed based on a sampled data model of the original switching dynamics and a linear quadratic criterion that takes the intersampling behavior into account.

  • 387. Baratchart, L.
    et al.
    Enqvist, Per
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Gombani, A.
    Olivi, M.
    Minimal symmetric Darlington synthesis2007In: MCSS. Mathematics of Control, Signals and Systems, ISSN 0932-4194, E-ISSN 1435-568X, Vol. 19, no 4, p. 283-311Article in journal (Refereed)
    Abstract [en]

    We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I (p)-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-p-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue.

  • 388. Zhong, J.
    et al.
    Karasalo, M.
    Cheng, D.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    New results on non-regular linearization of non-linear systems2007In: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 80, no 10, p. 1651-1664Article in journal (Refereed)
    Abstract [en]

    This paper presents some new results on non-regular linearization of non-linear systems. Based on a normal form and a non-regular linearization technique developed recently, the paper first provides a set of calculating formulas for the linearization procedure. As an application, the linearization of bilinear systems is investigated. Then, it presents easily veri. able sufficient conditions for the global (semi-global) (approximate) linearization. Finally, an estimate of the region of attraction for the kth degree approximately linearized systems with state feedback control is given, which illustrates one of the advantages of the approximate linearization.

  • 389. Cedervall, Simon
    et al.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Nonlinear observers for unicycle robots with range sensors2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 7, p. 1325-1329Article in journal (Refereed)
    Abstract [en]

    For nonlinear mobile systems equipped with exteroceptive sensors, the observability does not only depend on the initial conditions, but also on the control and the environment. This presents an interesting issue: how to design an observer together with the exciting control. In this note, the problem of designing an observer based on range sensor readings is studied. A design method based on periodic excitations is proposed for unicycle robotic systems.

  • 390.
    Gustavi, Tove
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Xiaoming, Hu
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Observer based leader-following formation control using on-board sensor information2007In: Proceedings of the 26th Chinese Control Conference, Vol 6 / [ed] Cheng, DZ; Wu, M, 2007, p. 752-755Conference paper (Refereed)
    Abstract [en]

    In this paper leader-following formation control for mobile multi-agent systems with limited sensor information is studied. The control algorithms developed require only information available from on-board sensors, and in particular, the measurement of the leader (neighbor) speed is not needed.

  • 391.
    Blomqvist, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the relation between weighted frequency-domain maximum-likelihood power spectral estimation and the prefiltered covariance extension approach2007In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 55, no 1, p. 384-389Article in journal (Refereed)
    Abstract [en]

    The aim of this correspondence is to study the connection between weighted frequency-domain maximum-likelihood power spectral estimation and the time-domain prefiltered covariance extension approach. Weighting and prefiltering are introduced to emphasize the model fit in a certain frequency range. The main result is that these two methods are very closely related for the case of autoregressive (AR) model estimation, which implies that both can be formulated as convex optimization problems. Examples illustrating the methods and the effect of prefiltering/weighting are provided.

  • 392.
    Fanizza, Giovanna
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Nagamune, Ryozo
    Univ British Columbia, Dept Mech Engn, Vancouver.
    Passivity-preserving model reduction by analytic interpolation2007In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 425, no 2-3, p. 608-633Article in journal (Refereed)
    Abstract [en]

    Antoulas and Sorensen have recently proposed a passivity-preserving model-reduction method of linear systems based on Krylov projections. The idea is to approximate a positive-real rational transfer function with one of lower degree. The method is based on an observation by Antoulas (in the single-input/single-output case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes, Georgiou and Lindquist, namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models. We also show that, in the multi-input/multi-output case, Sorensen's algorithm actually amounts to tangential Nevanlinna-Pick interpolation.

  • 393.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Prediction-error approximation by convex optimization2007In: Modeling, Estimation and Control:Festschrift in honor of Giorgio Picci on the occation of his sixty-fifth birthday, BERLIN: SPRINGER-VERLAG BERLIN , 2007, Vol. 364, p. 239-249Chapter in book (Refereed)
    Abstract [en]

    This paper is dedicated to Giorgio Picci on the occasion of his 65th birthday. I have come to appreciate Giorgio not only as a great friend but also as a great scholar. When we first met at Brown University in 1973, he introduced me to his seminal paper [29] on splitting subspaces, which became the impetus for our joint work on the geometric theory of linear stochastic systems [23,24,25,26]. This led to a life-long friendship and a book project that never seemed to converge, but now is close to being finished [27]. I have learned a lot from Giorgio. The present paper grew out of a discussion in our book project, when Giorgio taught me about the connections between prediction-error identification and the Kullback-Leibler criterion. These concepts led directly into the recent theory of analytic interpolation with complexity constraint, with which I have been deeply involved in recent times. I shall try to explain these connections in the following paper.

  • 394.
    Kuroiwa, Yohei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sensitivity shaping for systems with time delay by Nevanlinna-Pick interpolation2007In: PROCEEDINGS OF THE 46TH IEEE CONFERENCE ON DECISION AND CONTROL, 2007, p. 2821-2825Conference paper (Refereed)
    Abstract [en]

    It was pointed out by Foias, Tannenbaum and Zames that the unweighted H-infinity sensitivity optimization for systems with time delay can be formulated as a finite dimensional Nevanlinna-Pick interpolation. The purpose of this paper is to consider this formulation. The synthesis of the controller and the shaping of sensitivity function are carried out by the theory of Nevanlinna-Pick interpolation with degree constraint. It turns out that the controller has a structure of the Smith predictor. The finite impulse response system is only determined by non-minimum phase zeros and unstable poles of the plant.

  • 395.
    Svanberg, Krister
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Werme, Mats
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sequential integer programming methods for stress constrained topology optimization2007In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 34, no 4, p. 277-299Article in journal (Refereed)
    Abstract [en]

    This paper deals with topology optimization of load carrying structures defined on a discretized design domain where binary design variables are used to indicate material or void in the various finite elements. The main contribution is the development of two iterative methods which are guaranteed to find a local optimum with respect to a 1-neighbourhood. Each new iteration point is obtained as the optimal solution to an integer linear programming problem which is an approximation of the original problem at the previous iteration point. The proposed methods are quite general and can be applied to a variety of topology optimization problems defined by 0-1 design variables. Most of the presented numerical examples are devoted to problems involving stresses which can be handled in a natural way since the design variables are kept binary in the subproblems.

  • 396. Cheng, D.
    et al.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Set stability and controllability for switched non-homogeneous linear systems2007In: 2006 Chinese Control Conference Proceedings, CCC 2006, IEEE , 2007, p. 2171-2176Conference paper (Refereed)
    Abstract [en]

    In this paper we consider some control problems of switched non-homogeneous linear systems. First, the set stability of switched non-homogeneous linear systems is considered. It is proved that as the linear parts have a common quadratic Lyapunov function the set stability is assured. The problem of searching smallest attracting set is then considered. Then we assume the switching law is controllable and investigate the controllability condition within the attracting region. Finally, we consider the aggregation and the control of aggregation of flocking behavior. Particularly, the results obtained are implemented to analyzing and manipulating of a group of mobile robots.

  • 397.
    Fanizza, Giovanna
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Nagamune, Ryozo
    Univ British Columbia, Dept Mech Engn.
    Spectral estimation by least-squares optimization based on rational covariance extension2007In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 43, no 2, p. 362-370Article in journal (Refereed)
    Abstract [en]

    This paper proposes a new spectral estimation technique based on rational covariance extension with degree constraint. The technique finds a rational spectral density function that approximates given spectral density data under constraint on a covariance sequence. Spectral density approximation problems are formulated as nonconvex optimization problems with respect to a Schur polynomial. To formulate the approximation problems, the least-squares sum is considered as a distance. Properties of optimization problems and numerical algorithms to solve them are explained. Numerical examples illustrate how the methods discussed in this paper are useful in stochastic model reduction and stochastic process modeling.

  • 398.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung-Yao
    Univ Melbourne, Dept Elect & Elect Engn.
    Mari, Jorge
    GE Global Res, Elect Energy Syst.
    Stability analysis of a class of PWM systems2007In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 52, no 6, p. 1072-1078Article in journal (Refereed)
    Abstract [en]

    This note considers stability analysis of a class of pulsewidth modulated (PWM) systems that incorporates several different switched mode dc-de- converters. The systems of the class typically have periodic solutions. A sampled data model is developed and used to prove stability of these solutions. Conditions for global and local exponential stability are derived using quadratic and piecewise quadratic Lyapunov functions. The state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities (LMIs).

  • 399.
    Karlsson, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Stable rational approximation in the context of interpolation and convex optimization2007In: Proceedings Of The 46th IEEE Conference On Decision And Control, Vols 1-14, 2007, p. 2214-2221Conference paper (Refereed)
    Abstract [en]

    A quite comprehensive theory of analytic interpolation with degree constraint, dealing with rational interpolants with an a priori bound, has been developed in recent years. In this paper we consider the limit case when this bound is removed, and only stable interpolants with a prescribed maximum degree are sought. This leads to weighted H-2 minimization, where the interpolants are parameterized by the weights. The inverse problem of determining the weight and the interpolation points given a desired interpolant profile is considered, and a rational approximation procedure based on the theory is proposed. This provides a tool for tuning the solution to specifications. The basic idea could also be applied to the case with bounded interpolants.

  • 400. Zhu, Y.
    et al.
    Cheng, D.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Synchronization of a class of networked passive systems with switching topology2007In: Proceedings of the 46th IEEE Conference on Decision and Control, 2007, p. 2271-2276Conference paper (Refereed)
    Abstract [en]

    This paper considers the output synchronization of a class of networked agents. Each agent is a passive system. Local information, used by each agent to adjust its movement, forms a network with switching adjacent topology. First, we consider the asymptotic stability of nonlinear time-varying switched systems by using multiple Lyapunov function. An extended Lyapunov-like Lemma for switched systems is obtained. Then the result is applied to the output synchronization of a class of networked passive systems with switching topology. A pretty fair sufficient condition is presented.

567891011 351 - 400 of 521
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