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  • 301.
    Kuroiwa, Yohei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A positive partial realization of time series2009In: 17th European Signal Processing Conference (EUSIPCO 2009), 2009, p. 413-416Conference paper (Refereed)
    Abstract [en]

    For a given partial covariance sequence (C 0,C 1,⋯,C n) and for each MA part of the ARMA modeling filter of degree n, an AR part of the ARMA modeling filter of degree n for the solution to the rational covariance extension problem is obtained by solving a nonlinear equation, which is homotopic to a nonlinear equation determining the maximum entropy AR filter.

  • 302.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, Chung-Yao
    A Scalable Robust Stability Criterion for Systems with Heterogeneous LTI Components2009In: 2009 AMERICAN CONTROL CONFERENCE, 2009, p. 2898-2903Conference paper (Refereed)
    Abstract [en]

    A scalable robust stability criterion for networked interconnected systems with heterogeneous linear time-invariant components is presented in this paper. The criterion involves only the properties of individual components and the spectrum of the interconnection matrix, which can be verified with relatively low computational effort, and more importantly maintains scalability of the analysis. Moreover, if the components are single-input-single-output (SISO), the criterion has an appealing graphical interpretation which resembles the classical Nyquist criterion.

  • 303.
    Wang, Jinhuan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Cheng, Daizhan
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    An extension of LaSalle's Invariance Principle for a class of switched linear systems2009In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 58, no 10-11, p. 754-758Article in journal (Refereed)
    Abstract [en]

    In this paper LaSalle's Invariance Principle for switched linear systems is studied. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, in this paper the switching modes are allowed to be only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability of switched linear systems is proposed provided that the kernels of derivatives of a common quadratic Lyapunov function with respect to the switching modes are disjoint (except the origin).

  • 304.
    Karasalo, Maja
    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.
    An Optimization Approach to Adaptive Kalman Filtering2009In: 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009; Shanghai; 15 December 2009 through 18 December 2009; Category number 09CH38112; Code 79678, 2009, p. 2333-2338Conference paper (Refereed)
    Abstract [en]

    In this paper, an optimization-based adaptive Kalman filtering method is proposed. The method produces an estimate of the process noise covariance matrix Q by solving an optimization problem over a shortwindow of data. The algorithm recovers the observations h(x) from a system dot x = f(x), y = h(x) + v without a priori knowledge of system dynamics. Potential applications include target tracking using a network of nonlinear sensors, servoing, mapping, and localization. The algorithm isdemonstrated in simulations on a tracking example for a target with coupled and nonlinear kinematics.Simulations indicate superiority overa standard MMAE algorithm for a large class of systems.

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  • 305.
    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 Linear and Logarithmic Interpolation of Spectra2009Report (Other academic)
    Abstract [en]

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

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  • 306.
    Kuroiwa, Yohei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Block discrete-time schwarz form of multivariable rational interpolant and positivity by linear matrix inequality2009In: European Signal Processing Conference, 2009, p. 393-397Conference paper (Refereed)
    Abstract [en]

    The state-space realization of a multivariable rational interpolant with bounded McMillan degree is given by the block discrete-time Schwarz form. A characterization of the positive realness of the block discrete-time Schwarz form is given by a linear matrix inequality.

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  • 307. Kao, Chung-Yao
    et al.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Fujioka, Hisaya
    Characterization of robust stability of a class of interconnected systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 1, p. 217-224Article in journal (Refereed)
    Abstract [en]

    We consider robust stability analysis of a class of large scale interconnected systems. The individual subsystems may be different but they are assumed to share a property that characterizes a set of interconnection matrices which lead to stable overall systems. 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 low complexity problem of checking whether the frequency response of the individual subsystems and the eigenvalues of the interconnection matrix can be mutually separated using a class of quadratic forms. Most interestingly, it is shown that this criterion is also necessary, in the sense that if the criterion is violated, an interconnection matrix of the same eigenvalue distribution can be found to make the overall system unstable.

  • 308. Fujioka, H.
    et al.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Characterizing uncertain time-varying parameters with periodic reset2009In: 2009 American Control Conference, 2009, p. 3754-3756Conference paper (Refereed)
    Abstract [en]

    A number of quadratic constraints are derived for an uncertain real parameter which is slowly time-varying and periodically resetting. A finite-horizon version of the swapping lemma and a finite dimensional condition for computing the norm of related time-varying finite-horizon systems are derived.

  • 309.
    Aittokoski, Timo
    et al.
    Department of Mathematical Information Technology, University of Jyväskylä, Finland.
    Äyrämö, Sami
    Department of Mathematical Information Technology, University of Jyväskylä, Finland.
    Miettinen, Kaisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Clustering aided approach for decision making in computationally expensive multiobjective optimization2009In: Optimization Methods and Software, ISSN 1055-6788, E-ISSN 1029-4937, Vol. 24, no 2, p. 157-174Article in journal (Refereed)
    Abstract [en]

    Typically, industrial optimization problems need to be solved in an efficient, multiobjective and global manner, because they are often computationally expensive (as function values are typically based on simulations), they may contain multiple conflicting objectives, and they may have several local optima. Solving such problems may be challenging and time consuming when the aim is to find the most preferred Pareto optimal solution.

    In this study, we propose a method where we use an advanced clustering technique to reveal essential characteristics of the approximation of the Pareto optimal set, which has been generated beforehand. Thus, the decision maker (DM) is involved only after the most time consuming computation is finished. After the initiation phase, a moderate number of cluster prototypes projected to the Pareto optimal set is presented to the DM to be studied. This allows him/her to rapidly gain an overall understanding of the main characteristics of the problem without placing too much cognitive load on the DM. Furthermore, we also suggest some ways of applying our approach to different types of problems and demonstrate it with an example related to internal combustion engine design.

  • 310.
    Wang, Jinhuan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Hebei University of Technology, China.
    Liu, Z.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Consensus of high order linear multi-agent systems using output error feedback2009In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009, IEEE , 2009, p. 3685-3690Conference paper (Refereed)
    Abstract [en]

    In this paper, we study the consensus problem of multi-agent systems in which each agent adopts the same linear model that can be of any order. We consider the case where only the relative output error between the neighboring agents can be measured. In order to solve the consensus problem, two kinds of decentralized control laws are designed. We first show that a static output error feedback control can solve the consensus problem if some further constraints on the system model is imposed. Then we use an observer based approach to design a dynamic output error feedback consensus control. We note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.

  • 311.
    Karasalo, Maja
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Piccolo, Giacomo
    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 - Algorithms and Experimental Validation2009In: Robotics and Autonomous Systems, ISSN 0921-8890, E-ISSN 1872-793X, Vol. 57, no 6-7, p. 617-628Article in journal (Refereed)
    Abstract [en]

    In this paper, a recursive smoothing splineapproach for contour reconstruction is studied and evaluated.  Periodic smoothing splines areused by a robot to approximate the contour of encountered obstaclesin the environment.  The splines are generated through minimizing acost function subject to constraints imposed by a linear controlsystem and accuracy is improved iteratively using a recursive splinealgorithm.  The filtering effect of the smoothing splines allows forusage of noisy sensor data and the method is robust with respect to odometrydrift. The algorithm is extensively evaluated in simulationsfor various contours and in experiments using a SICK laser scanner mounted on a PowerBot fromActivMedia Robotics

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  • 312.
    Gustavi, Tove
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Control and coordination of mobile multi-agent systems2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, various control problems originating from the field of mobile robotics are considered. In particular, the thesis deals with problems that are related to the interaction and coordination of multiple mobile units. The scientific contributions are presented in five papers that together constitute the main part of the thesis. The papers are preceded by a longer introductory part, in which some important results from control theory, data processing and robotics are reviewed.

    In the first of the appended papers, two stabilizing tracking controls are proposed for a non-holonomic robot platform of unicycle type. Tolerance to errors and other properties of the controllers are discussed and a reactive obstacle avoidance control, that can easily be incorporated with the proposed tracking controls, is suggested. In Paper B, the results from Paper~A are extended to multi-agent systems. It is demonstrated how the tracking controls from Paper A can be used as building blocks when putting together formations of robots, in which each robot maintains a fixed position relative its neighbors during translation. In addition, switching between the different control functions is shown to be robust, implying that it is possible to change the shape of a formation on-line.

    In the first two papers, the tracking problem is facilitated by the assumption that the approximate velocity of the target/leader is known to the tracking robot. Paper C treats the the case where the target velocity is neither directly measurable with the available sensor setup, nor possible to obtain through communication with neighboring agents. Straight-forward computation of the target velocity from available sensor data unfortunately tend to enhance measurement errors and give unreliable estimates. To overcome the difficulties, an alternative approach to velocity estimation is proposed, motivated by the local observability of the given control system.

    Paper D deals with another problematic aspect of data acquisition. When using range sensors, one often obtains a mixed data set with measurements originating from many different sources. This problem would, for instance, be encountered by a robot moving in a formation, where it was surrounded by other agents. There exist established techniques for sorting mixed data sets off-line, but for time-depending systems where data need to be sorted on-line and only small time delays can be tolerated, established methods fail. The solution presented in the paper is a prediction-correction type algorithm, referred to as CCIA (Classification Correction and Identification algorithm).

    Finally, in Paper E, we consider the problem of maintaining connectivity in a multi-agent system. Often inter-agent communication abilities are associated with some proximity constraints, so when the robots move in relation to each other, communication links both break and form. In the paper we present a framework for analysis that makes it possible to compute a set of general constraints which, if satisfied, are sufficient to guarantee maintained communication for a given multi-agent system. Constraints are computed for two sorts of consensus-based systems and the results are verified in simulations.

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  • 313.
    Karasalo, Maja
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Data Filtering and Control Design for Mobile Robots2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis, we consider problems connected to navigation and tracking for autonomousrobots under the assumption of constraints on sensors and kinematics. We study formation controlas well as techniques for filtering and smoothing of noise contaminated input. The scientific contributions of the thesis comprise five papers.In Paper A, we propose three cascaded, stabilizing formation controls for multi-agent systems.We consider platforms with non-holonomic kinematic constraints and directional rangesensors. The resulting formation is a leader-follower system, where each follower agent tracksits leader agent at a specified angle and distance. No inter-agent communication is required toexecute the controls. A switching Kalman filter is introduced for active sensing, and robustnessis demonstrated in experiments and simulations with Khepera II robots.In Paper B, an optimization-based adaptive Kalman filteringmethod is proposed. The methodproduces an estimate of the process noise covariance matrix Q by solving an optimization problemover a short window of data. The algorithm recovers the observations h(x) from a system˙ x = f (x), y = h(x)+v without a priori knowledge of system dynamics. The algorithm is evaluatedin simulations and a tracking example is included, for a target with coupled and nonlinearkinematics. In Paper C, we consider the problem of estimating a closed curve in R2 based on noisecontaminated samples. A recursive control theoretic smoothing spline approach is proposed, thatyields an initial estimate of the curve and subsequently computes refinements of the estimateiteratively. Periodic splines are generated by minimizing a cost function subject to constraintsimposed by a linear control system. The optimal control problem is shown to be proper, andsufficient optimality conditions are derived for a special case of the problem using Hamilton-Jacobi-Bellman theory.Paper D continues the study of recursive control theoretic smoothing splines. A discretizationof the problem is derived, yielding an unconstrained quadratic programming problem. Aproof of convexity for the discretized problem is provided, and the recursive algorithm is evaluatedin simulations and experiments using a SICK laser scanner mounted on a PowerBot from ActivMedia Robotics. Finally, in Paper E we explore the issue of optimal smoothing for control theoretic smoothingsplines. The output of the control theoretic smoothing spline problem is essentially a tradeoff between faithfulness to measurement data and smoothness. This tradeoff is regulated by the socalled smoothing parameter. In Paper E, a method is developed for estimating the optimal valueof this smoothing parameter. The procedure is based on general cross validation and requires noa priori information about the underlying curve or level of noise in the measurements.

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  • 314. Hu, J.
    et al.
    Hong, Y.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Distributed shift target estimation using multiple cooperative agents2009In: Proceedings of 2009 7th Asian Control Conference, ASCC 2009, 2009, p. 117-122Conference paper (Refereed)
    Abstract [en]

    In this paper we discuss the estimation of a moving target by cooperative agents equipped with sensors. To locate a moving target, a distributed algorithm is given for the networked agents based on a time-based shift. A nonlinear filter with fusing collected sensor information is proposed to estimate the trajectory of the target with unknown dynamics. The convergence of the estimation in the sensor network is analyzed and proved via a theoretic approach.

  • 315.
    Almér, Stefan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dynamic Phasor Analysis of Periodic Systems2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 8, p. 2007-2012Article in journal (Refereed)
    Abstract [en]

    The paper considers stability analysis of linear time-periodic (LTP) systems based on the dynamic phasor model (DPM). The DPM exploits the periodicity of the system by expanding the system state in a Fourier series over a moving time window. This results in an L-2-equivalent representation in terms of an infinite-dimensional LTI system which describes the evolution of time varying Fourier coefficients. To prove stability, we consider quadratic time-periodic Lyapunov candidates. Using the DPM, the corresponding time-periodic Lyapunov inequality can be stated as a finite dimensional inequality and the Lyapunov function can be found by solving a linear matrix inequality.

  • 316.
    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.
    Harmonic analysis of pulse-width modulated systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 4, p. 851-862Article in journal (Refereed)
    Abstract [en]

    The paper considers the so-called dynamic phasor model as a basis for harmonic analysis of a class switching systems. The analysis covers both periodically switched systems and non-periodic systems where the switching is controlled by feedback. The dynamic phasor model is a powerful tool for exploring cyclic properties of dynamic systems. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems.

  • 317.
    Byrnes, Christopher
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). KTH, School of Engineering Sciences (SCI), Centres, Center for Industrial and Applied Mathematics, CIAM.
    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.
    Important moments in systems, control and optimizations2009In: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on, IEEE , 2009, p. 91-96Conference paper (Refereed)
    Abstract [en]

    The moment problem matured from its various special forms in the late 19th and early 20th Centuries to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. In particular, the theory of systems and control is no exception, where the applications have historically been to circuit theory, optimal control, robust control, signal processing, spectral estimation, stochastic realization theory and the use of the moments of a probability density. Many of these applications are also still works in progress. In this paper, we consider the generalized moment problem, expressed in terms of a basis of a finite-dimensional subspace β of the Banach space C[a, b] and a "positive" sequences c, but with a new wrinkle inspired by the applications to systems and control. We seek to parameterize solutions which are positive "rational" measures, in a suitably generalized sense. Our parameterization is given in terms of smooth objects. In particular, the desired solution space arises naturally as a manifold which can be shown to be diffeomorphic to a Euclidean space and which is the domain of some canonically defined functions. Moreover, on these spaces one can derive natural convex optimization criteria which characterize solutions to this new class of moment problems.

  • 318. Cantoni, M.
    et al.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Kao, C. -Y
    IQC robustness analysis for feedback interconnections of unstable distributed parameter systems2009In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009, IEEE , 2009, p. 1124-1130Conference paper (Refereed)
    Abstract [en]

    In recent work the authors combined integral-quadratic-constraint (IQC) based analysis with ν-gap metric based analysis to study the robustness of feedback interconnections of possibly unstable rational transfer functions. This is extended here to the case of irrational transfer functions without pure delays. Specifically, we restrict attention to the sub-algebra of Callier-Desoer class transfer functions that have a limit at infinity.

  • 319.
    Georgiou, Tryphon T.
    et al.
    Department of Electrical Engineering, University of Minnesota.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Takyar, Mir Shahrouz
    Department of Electrical Engineering, University of Minnesota.
    Metrics for Power Spectra: An Axiomatic Approach2009In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 3, p. 859-867Article in journal (Refereed)
    Abstract [en]

    We present an axiomatic framework for seeking distances between power spectral density functions. The axioms require that the sought metric respects the effects of additive and multiplicative noise in reducing our ability to discriminate spectra, as well as they require continuity of statistical quantities with respect to perturbations measured in the metric. We then present a particular metric which abides by these requirements. The metric is based on the Monge-Kantorovich transportation problem and is contrasted with an earlier Riemannian metric based on the minimum-variance prediction geometry of the underlying time-series. It is also being compared with the more traditional Itakura-Saito distance measure, as well as the aforementioned prediction metric, on two representative examples.

  • 320.
    Anisi, David A.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On Cooperative Surveillance, Online Trajectory Planning and Observer Based Control2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    The main body of this thesis consists of six appended papers. In the  first two, different  cooperative surveillance problems are considered. The second two consider different aspects of the trajectory planning problem, while the last two deal with observer design for mobile robotic and Euler-Lagrange systems respectively.In Papers A and B,  a combinatorial optimization based framework to cooperative surveillance missions using multiple Unmanned Ground Vehicles (UGVs) is proposed. In particular, Paper A  considers the the Minimum Time UGV Surveillance Problem (MTUSP) while Paper B treats the Connectivity Constrained UGV Surveillance Problem (CUSP). The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from  a point on a waypoint-path and such that the time for executing the search in parallel is minimized.  The connectivity constrained formulation  extends the MTUSP by additionally requiring the induced information graph to be  kept recurrently connected  at the time instants when the UGVs  perform the surveillance mission.  In these two papers, the NP-hardness of  both these problems are shown and decomposition techniques are proposed that allow us to find an approximative solution efficiently in an algorithmic manner.Paper C addresses the problem of designing a real time, high performance trajectory planner for an aerial vehicle that uses information about terrain and enemy threats, to fly low and avoid radar exposure on the way to a given target. The high-level framework augments Receding Horizon Control (RHC) with a graph based terminal cost that captures the global characteristics of the environment.  An important issue with RHC is to make sure that the greedy, short term optimization does not lead to long term problems, which in our case boils down to two things: not getting into situations where a collision is unavoidable, and making sure that the destination is actually reached. Hence, the main contribution of this paper is to present a trajectory planner with provable safety and task completion properties. Direct methods for trajectory optimization are traditionally based on a priori temporal discretization and collocation methods. In Paper D, the problem of adaptive node distribution is formulated as a constrained optimization problem, which is to be included in the underlying nonlinear mathematical programming problem. The benefits of utilizing the suggested method for  online  trajectory optimization are illustrated by a missile guidance example.In Paper E, the problem of active observer design for an important class of non-uniformly observable systems, namely mobile robotic systems, is considered. The set of feasible configurations and the set of output flow equivalent states are defined. It is shown that the inter-relation between these two sets may serve as the basis for design of active observers. The proposed observer design methodology is illustrated by considering a  unicycle robot model, equipped with a set of range-measuring sensors. Finally, in Paper F, a geometrically intrinsic observer for Euler-Lagrange systems is defined and analyzed. This observer is a generalization of the observer proposed by Aghannan and Rouchon. Their contractivity result is reproduced and complemented  by  a proof  that the region of contraction is infinitely thin. Moreover, assuming a priori bounds on the velocities, convergence of the observer is shown by means of Lyapunov's direct method in the case of configuration manifolds with constant curvature.

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  • 321.
    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.
    On Degree-Constrained Analytic Interpolation With Interpolation Points Close to the Boundary2009In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 54, no 6, p. 1412-1418Article in journal (Refereed)
    Abstract [en]

    In the recent article [4], a theory for complexity-constrained interpolation of contractive functions is developed. In particular, it is shown that any such interpolant may be obtained as the unique minimizer of a (convex) weighted entropy gain. In this technical note we study this optimization problem in detail and describe how the minimizer depends on weight selection and on interpolation conditions. We first show that, if, for a sequence of interpolants, the values of the entropy gain of the interpolants converge to the optimum, then the interpolants converge in H-2, but not in H-infinity This result is then used to describe the asymptotic behavior of the interpolant as an interpolation point approaches the boundary of the domain of analyticity. For loop shaping to specifications in control design, it might at first seem natural to place strategically additional interpolation points close to the boundary. However, our results indicate that such a strategy will have little effect on the shape. Another consequence of our results relates to model reduction based on minimum-entropy principles, where one should avoid placing interpolation points too close to the boundary.

  • 322.
    Sandberg, Henrik
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    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.
    Karlsson, Gunnar
    KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl H.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On performance limitations of congestion control2009In: Proceedings of the IEEE Conference on Decision and Control, 2009, p. 5869-5876Conference paper (Refereed)
    Abstract [en]

    Fundamental performance limitations on congestion control is discussed in relation to the information that is available in the controller. Three control architectures that all use bottle-neck buffer delay information of various form as inputs and sending rate as outputs are considered. It is shown that feedback delays from buffer to senders set limits on the achievable performance measured through fairness, efficiency and stability. We apply our findings to TCP FAST and can make some new interesting control theoretic interpretations of that protocol.

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  • 323.
    Gustavi, Tove
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Dimarogonas, Dimos V.
    Egerstedt, Magnus
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    On the Number of Leaders Needed to Ensure Network Connectivity in Arbitrary Dimensions2009In: MED: 2009 17TH MEDITERRANEAN CONFERENCE ON CONTROL & AUTOMATION, VOLS 1-3, NEW YORK: IEEE , 2009, p. 98-103Conference paper (Refereed)
    Abstract [en]

    We examine the leader-to-follower ratio needed to maintain connectivity in a leader-follower multi-agent network with proximity based communication topology. The paper extends the one-dimensional results of [2] to the two dimensional case. In the scenario we consider, only the leaders are aware of the global mission, which is to converge to a known destination point. Thus, the objective of the leaders is to drag the team to the desired goal. In the paper we obtain bounds on the number of leaders needed to complete the task. The results are first established for an initially complete communication graph and then extended to the incomplete case. Computer simulations support the derived theory.

  • 324.
    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.
    On the validity of using small positive lower bounds on design variables in discrete topology optimization2009In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 37, no 4, p. 325-334Article in journal (Refereed)
    Abstract [en]

    It is proved that an optimal {epsilon, 1}(n) solution to a "epsilon-perturbed" discrete minimum weight problem with constraints on compliance, von Mises stresses and strain energy densities, is optimal, after rounding to {0, 1}(n), to the corresponding "unperturbed" discrete problem, provided that the constraints in the perturbed problem are carefully defined and epsilon > 0 is sufficiently small.

  • 325. Kragelund, M.
    et al.
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Leth, J.
    Wisniewski, R.
    Optimal production planning of a power plant2009In: 2009 IEEE International Conference on Control and Automation, ICCA 2009, IEEE , 2009, p. 819-824Conference paper (Refereed)
    Abstract [en]

    This paper addresses the problem of planning the usage of actuators optimally in an economic perspective. The objective is to maximize the profit of operating a given plant during 24 hours of operation. Models of two business objectives are formulated in terms of system states and the monetary value of these objectives is established. Based on these and the cost of using the different actuators a profit function has been formulated. The optimization of the profit is formulated as an optimal control problem where the constraints include the dynamics of the plant as well as a requirement to reference tracking. A power plant is considered in this paper, where the fuel system consists of three different fuels; coal, gas, and oil.

  • 326. Fujioka, Hisaya
    et al.
    Kao, Chung-Yao
    Almér, Stefan
    Jönsson, Ulf
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Robust tracking with H-infinity performance for PWM systems2009In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 45, no 8, p. 1808-1818Article in journal (Refereed)
    Abstract [en]

    Control synthesis for robust tracking is considered for a class of pulse-width modulated systems that appear, for example, in power electronics applications. The control objective is to regulate a high frequency ripple signal to robustly track a constant reference signal in an average sense. To achieve this goal, a new H-infinity control problem with integral action and average sampling is proposed. The solution of this problem involves a hybrid lifting framework which requires a careful elaboration in order to develop an algorithm that allows one to solve the design problem by the standard state space formulas for H-infinity control. The design procedure is verified on a synchronous buck converter.

  • 327.
    Möller, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Stability of high order distributed power control2009In: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on, IEEE , 2009, p. 4963-4970Conference paper (Refereed)
    Abstract [en]

    There are several proposed algorithms for distributed power control of wireless networks. In this article an extended algorithm including high order dynamics is discussed and sufficient conditions for stability are derived. The stability analysis is first made using analysis in linear scale and then with logarithmized variables in a control theoretic approach, using both input-output and Lyapunov theory.

  • 328. Byrnes, Christopher I.
    et al.
    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.
    The moment problem for rational measures: convexity in the spirit of Krein2009In: MODERN ANALYSIS AND APPLICATIONS: MARK KREIN CENTENARY CONFERENCE / [ed] Adamyan, V; Berezansky, Y; Gohberg, I; Gorbachuk, M; Gorbachuk, V; Kochubei, A; Langer, H; Popov, G, Birkhäuser Verlag, 2009, Vol. 190, p. 157-169Conference paper (Refereed)
    Abstract [en]

    The moment problem as formulated by Krein and Nudel'man is a beautiful generalization of several important classical moment problems, including the power moment problem, the trigonometric moment problem and the moment problem arising in Nevanlinna-Pick interpolation. Motivated by classical applications and examples, in both finite and infinite dimensions, we recently formulated a new version of this problem that we call the moment problem for positive rational measures. The formulation reflects the importance of rational functions in signals, systems and control. While this version of the problem is decidedly nonlinear, the basic tools still rely on convexity. In particular, we present a solution to this problem in terms of a nonlinear convex optimization problem that generalizes the maximum entropy approach used in several classical special cases.

  • 329. Liu, Z.
    et al.
    Han, J.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    The number of leaders needed for consensus2009In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009, IEEE , 2009, p. 3745-3750Conference paper (Refereed)
    Abstract [en]

    In order to have a self-organized multi-agent system exhibit some expected collective behavior, it is necessary that some agents (called leaders) are informed about the expected behavior and able to intervene. Then a fundamental question is: how many such leaders are needed? Naturally the answer depends on the model used. In this paper the model proposed by Vicsek et al. is used for the analysis. By analyzing the system dynamics and estimating the characteristics of the initial neighbor graph, a lower bound on the ratio of leaders is provided that guarantees the expected consensus being reached almost surely.

  • 330.
    Miettinen, Kaisa
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hakanen, Jussi
    Why Use Interactive Multi-Objective Optimization in Chemical Process Design?2009In: Multi-objective optimization: techniques and applications in chemical engineering / [ed] G. P. Rangaiah, Singapore: World Scientific, 2009, p. 153-188Chapter in book (Other academic)
  • 331.
    Kuroiwa, Yohei
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A complete parameterization of all rational covariance extensions2008In: Proceedings of 18th International Symposium of Mathematical Theory of Networks and Systems, 2008Conference paper (Other academic)
  • 332.
    Carlsson, Fredrik
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A conjugate-gradient based approach for approximate solutions of quadratic programs2008Report (Other academic)
    Abstract [en]

    This paper deals with numerical behaviour and convergence properties of a recently presented column generation approach for optimization of so called step-and-shoot radiotherapy treatment plans. The approach and variants of it have been reported to be efficient in practice, finding near-optimal solutions by generating only a low number of columns. The impact of different restrictions on the columns in a column generation method is studied, and numerical results are given for quadratic programs corresponding to three patient cases. In particular, it is noted that with a bound on the two-norm of the columns, the method is equivalent to the conjugate-gradient method. Further, the above-mentioned column generation approach for radiotherapy is obtained by employing a restriction based on the infinity-norm and non-negativity. The column generation method has weak convergence properties if restricted to generating feasible step-and-shoot plans, with a "tailing-off" effect for the objective values. However, the numerical results demonstrate that, like the conjugate-gradient method, a rapid decrease of the objective value is obtained in the first few iterations. For the three patient cases, the restriction on the columns to generate feasible step-and-shoot plans has small effect on the numerical efficiency.

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  • 333. Georgiou, Tryphon T.
    et al.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A convex optimization approach to ARMA modeling2008In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, no 5, p. 1108-1119Article in journal (Refereed)
    Abstract [en]

    We formulate a convex optimization problem for approximating any given spectral density with a rational one having a prescribed number of poles and zeros (n poles and m zeros inside the unit disc and their conjugates). The approximation utilizes the Kullback-Leibler divergence as a distance measure. The stationarity condition for optimality requires that the approximant matches n + 1 covariance moments of the given power spectrum and m cepstral moments of the corresponding logarithm, although the latter with possible slack. The solution coincides with one derived by Byrnes, Enqvist, and Lindquist who addressed directly the question of covariance and cepstral matching. Thus, the present paper provides an approximation theoretic justification of such a problem. Since the approximation requires only moments of spectral densities and of their logarithms, it can also be used for system identification.

  • 334. Byrnes, Christopher I.
    et al.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A note on the Jacobian conjecture2008In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 136, no 9, p. 3007-3011Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the Jacobian conjecture for a map f of complex a. ne spaces of dimension n. It is well known that if f is proper, then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if f is proper onto its image.

  • 335.
    Jönsson, Ulf T.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A SECTOR CONDITION FOR LIMIT CYCLE ROBUSTNESS2008In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 47, no 6, p. 2745-2772Article in journal (Refereed)
    Abstract [en]

    Robustness of periodic oscillations in autonomous feedback systems is 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 range. The quadratic constraint is generated as a time-periodic sector condition that characterizes the nonlinearity around 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.

  • 336. Cheng, Daizhan
    et al.
    Wang, Jinhuan
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    An extension of LaSalle's invariance principle and its application to multi-agent consensus2008In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 53, no 7, p. 1765-1770Article in journal (Refereed)
    Abstract [en]

    In the paper, an extension of LaSalle's Invariance Principle to a class of switched linear systems is studied. One of the motivations is the consensus problem in multi-agent systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability is obtained. Then it is used to solve the consensus reaching problem of certain multi-agent systems in which each agent is modeled by a double integrator, and the associated interaction graph is switching and is assumed to be only jointly connected.

  • 337.
    Jönsson, Ulf T.
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Megretski, Alexandre
    Analysis and computation of limit cycles for systems with separable nonlinearities2008In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 69, no 12, p. 4674-4693Article in journal (Refereed)
    Abstract [en]

    The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only a unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.

  • 338.
    Carlsson, Fredrik
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Combining segment generation with direct step-and-shoot optimization in intensity-modulated radiation therapy2008In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 35, no 9, p. 3828-3838Article in journal (Refereed)
    Abstract [en]

    A method for generating a sequence of intensity-modulated radiation therapy step-and-shoot plans with increasing number of segments is presented. The objectives are to generate high-quality plans with few, large and regular segments, and to make the planning process more intuitive. The proposed method combines segment generation with direct step-and-shoot optimization, where leaf positions and segment weights are optimized simultaneously. The segment generation is based on a column generation approach. The method is evaluated on a test suite consisting of five head-and-neck cases and five prostate cases, planned for delivery with an Elekta SLi accelerator. The adjustment of segment shapes by direct step-and-shoot optimization improves the plan quality compared to using fixed segment shapes. The improvement in plan quality when adding segments is larger for plans with few segments. Eventually, adding more segments contributes very little to the plan quality, but increases the plan complexity. Thus, the method provides a tool for controlling the number of segments and, indirectly, the delivery time. This can support the planner in finding a sound trade-off between plan quality and treatment complexity.

  • 339.
    Forsgren, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Comments on: Intensity modulated radiation therapy treatment plan optimization2008In: TOP - An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN 1134-5764, E-ISSN 1863-8279, Vol. 16, no 2, p. 246-247Article in journal (Refereed)
  • 340. Wang, Jinhuan
    et al.
    Cheng, Daizhan
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Consensus of multi-agent linear dynamic systems2008In: Asian journal of control, ISSN 1561-8625, E-ISSN 1561-8625, Vol. 10, no 2, p. 144-155Article in journal (Refereed)
    Abstract [en]

    In this paper the consensus problem is considered for multi-agent systems, in which all agents have an identical linear dynamic mode that can be of any order. The main result is that if the adjacent topology of the graph is frequently connected then the consensus is achievable via local-information-based decentralized controls, provided that the linear dynamic mode is completely controllable. Consequently, many existing results become particular cases of this general result. In this paper, the case of fixed connected topology is discussed first. Then the case of switching connected topology is considered. Finally, the general case is studied where the graph topology is switching and only connected often enough.

  • 341.
    Zhong, Jianghua
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kleijn, W. Bastiaan
    KTH, School of Electrical Engineering (EES), Sound and Image Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kozica, Ermin
    KTH, School of Electrical Engineering (EES), Sound and Image Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Constructive camera pose control for optimizing multiview distributed video coding2008In: Proceedings of the IEEE Conference on Decision and Control, 2008, p. 3372-3379Conference paper (Refereed)
    Abstract [en]

    In this paper camera pose control for optimizing multiview distributed video coding is considered. The scenario considered is that multiple agents with monocular cameras observe a common scene in a three dimensional world. To get a good video reconstruction under a transmission rate constraint, the camera closest to the center of the camera array is chosen as the reference camera. The poses of all other cameras are controlled and designed such that their images are maximally similar under a constraint on their separation. Based on the rigid motion allowed for the cameras, two cases are considered. For the case where the rigid motion only involves translation, translation control is designed. For the case where it involves both translation and rotation, both controls are constructed. Some simulated results are given to show the efficiency of the designed controllers.

  • 342. Zhong, Jianghua
    et al.
    Cheng, Daizhan
    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.
    Constructive stabilization for quadratic input nonlinear systems2008In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 44, no 8, p. 1996-2005Article in journal (Refereed)
    Abstract [en]

    In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions. the feasible control set is parameterized, and Continuous feedback stabilizing controls are designed. Then for the general case. piecewise Continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.

  • 343. Zhong, Jianghua
    et al.
    Cheng, Daizhan
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    CONSTRUCTIVE STABILIZATION OF QUADRATIC-INPUT NONLINEAR SYSTEMS WITH BOUNDED CONTROLS2008In: Journal of dynamical and control systems, ISSN 1079-2724, E-ISSN 1573-8698, Vol. 14, no 4, p. 571-593Article in journal (Refereed)
    Abstract [en]

    In this paper, the stabilization of quadratic-input nonlinear systems with bounded controls is considered. According to the type of quadratic-input forms, two cases, namely, positive definite and positive semi-definite, are considered. For the case of positive definiteness, a universal formula for bounded stabilizers is given via a known Lyapunov control function. For the case of positive semidefiniteness, a constructive parametrization of bounded stabilizers is proposed under the assumption that there exists a known Lyapunov control function with respect to a smaller control set than the admissible control set.

  • 344.
    Almér, Stefan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Control and Analysis of Pulse-Modulated Systems2008Doctoral thesis, comprehensive summary (Other scientific)
    Abstract [en]

    The thesis consists of an introduction and four appended papers. In the introduction we give an overview of pulse-modulated systems and provide a few examples of such systems. Furthermore, we introduce the so-called dynamic phasor model which is used as a basis for analysis in two of the appended papers. We also introduce the harmonic transfer function and finally we provide a summary of the appended papers.

    The first paper considers stability analysis of a class of pulse-width modulated systems based on a discrete time model. The systems considered typically have periodic solutions. Stability of a periodic solution is equivalent to stability of a fixed point of a discrete time model of the system dynamics.

    Conditions for global and local exponential stability of the discrete time model are derived using quadratic and piecewise quadratic Lyapunov functions. A griding procedure is used to develop a systematic method to search for the Lyapunov functions.

    The second paper considers the dynamic phasor model as a tool for stability analysis of a general class of pulse-modulated systems. The analysis covers both linear time periodic systems and systems where the pulse modulation is controlled by feedback. The dynamic phasor model provides an $\textbf{L}_2$-equivalent description of the system dynamics in terms of an infinite dimensional dynamic system. The infinite dimensional phasor system is approximated via a skew truncation. The truncated system is used to derive a systematic method to compute time periodic quadratic Lyapunov functions.

    The third paper considers the dynamic phasor model as a tool for harmonic analysis of a class of pulse-width modulated systems. The analysis covers both linear time periodic systems and non-periodic systems where the switching is controlled by feedback. As in the second paper of the thesis, we represent the switching system using the L_2-equivalent infinite dimensional system provided by the phasor model. It is shown that there is a connection between the dynamic phasor model and the harmonic transfer function of a linear time periodic system and this connection is used to extend the notion of harmonic transfer function to describe periodic solutions of non-periodic systems. The infinite dimensional phasor system is approximated via a square truncation. We assume that the response of the truncated system to a periodic disturbance is also periodic and we consider the corresponding harmonic balance equations. An approximate solution of these equations is stated in terms of a harmonic transfer function which is analogous to the harmonic transfer function of a linear time periodic system. The aforementioned assumption is proved to hold for small disturbances by proving the existence of a solution to a fixed point equation. The proof implies that for small disturbances, the approximation is good.

    Finally, the fourth paper considers control synthesis for switched mode DC-DC converters. The synthesis is based on a sampled data model of the system dynamics. The sampled data model gives an exact description of the converter state at the switching instances, but also includes a lifted signal which represents the inter-sampling behavior. Within the sampled data framework we consider H-infinity control design to achieve robustness to disturbances and load variations. The suggested controller is applied to two benchmark examples; a step-down and a step-up converter. Performance is verified in both simulations and in experiments.

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  • 345. Anisi, David A.
    et al.
    Ögren, Petter
    KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Lindskog, Therese
    Cooperative Surveillance Missions with Multiple Unmanned Ground Vehicles (UGVs)2008In: 47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008), 2008, p. 2444-2449Conference paper (Refereed)
    Abstract [en]

    This paper proposes an optimization based approach to multi-UGV surveillance. In particular, we formulate both the minimum time- and connectivity constrained surveillance problems, show NP-hardness of them and propose decomposition techniques that allow us to solve them efficiently in an algorithmic manner. The minimum time formulation is the following. Given a set of surveillance UGVs and a polyhedral area, find waypoint-paths for all UGVs such that every point of the area is visible from a point on a path and such that the time for executing the search in parallel is minimized. Here, the sensor's field of view are assumed to be occluded by the obstacles and limited by a maximal sensor range. The connectivity constrained formulation extends the first by additionally requiring that the information graph induced by the sensors is connected at the time instants when the UGVs stop to perform the surveillance task. The second formulation is relevant to situation when mutual visibility is needed either to transmit the sensor data being gathered, or to protect the team from hostile persons trying to approach the stationary UGVs.

  • 346.
    Aittokoski, Timo
    et al.
    Department of Mathematical Information Technology, University of Jyväskylä, Finland.
    Miettinen, Kaisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Cost Effective Simulation-Based Multiobjective Optimization in Performance of Internal Combustion Engine2008In: Engineering optimization (Print), ISSN 0305-215X, E-ISSN 1029-0273, Vol. 40, no 7, p. 593-612Article in journal (Refereed)
    Abstract [en]

    Solving real-life engineering problems requires often multiobjective, global, and efficient (in terms of objective function evaluations) treatment. In this study, we consider problems of this type by discussing some drawbacks of the current methods and then introduce a new population-based multiobjective optimization algorithm UPS-EMOA which produces a dense (not limited to the population size) approximation of the Pareto-optimal set in a computationally effective manner.

  • 347.
    Hu, Jiangping
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Hong, Yiguang
    Feng, Gang
    Distributed dynamic control for leaderless multi-agent consensus with star-like topology2008In: Asian journal of control, ISSN 1561-8625, E-ISSN 1561-8625, Vol. 10, no 2, p. 233-237Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider a consensus problem of a group of mobile agents interconnected by a star-like topology. Not all the state variables of the agent in the center of the group are available for its neighbors. A distributed controller together with a local state-estimation rule is given for each agent who has to estimate the unmeasurable velocity. Then, with help of virtual equivalent agents, we prove that, with the proposed control scheme, the group of agents can reach its consensus.

  • 348. Häll, C. H.
    et al.
    Högberg, Magdalena
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Effects of distance estimation methods in dial-a-ride planning2008In: Proceedings of the 13th International Conference of Hong Kong Society for Transportation Studies: Transportation and Management Science, Hong Kong Society for Transportation Studies (HKSTS), 2008, p. 751-759Conference paper (Refereed)
    Abstract [en]

    Paratransit in form of dial-a-ride service is widely used in Sweden. A main planning system in Sweden uses pre-calculated distance matrices, based on aggregated geographical zones. A trip between two zones is thereby assumed to take a certain time independent of where in the zones the actual pick-up and drop-off points are located. The aim of this paper is to examine the effects of using address-based shortest path calculations instead of zone-based distance estimates. A simulation environment is implemented in C#.Net, based on a standard formulation of the dynamic dial-a-ride problem, and simulations have been performed on historical data from the city of Göteborg. To evaluate the solutions, it is not adequate to evaluate only the objective function value, since a lower estimation of the distances will likely give a lower objective function value. Therefore we also discuss how to evaluate different solutions in other terms than objective function values.

  • 349. Byrnes, Christopher I.
    et al.
    Lindquist, Anders
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    IMPORTANT MOMENTS IN SYSTEMS AND CONTROL2008In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 47, no 5, p. 2458-2469Article in journal (Refereed)
    Abstract [en]

    The moment problem matured from its various special forms in the late 19th and early 20th centuries to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. In particular, the theory of systems and control is no exception, where the applications have historically been to circuit theory, optimal control, robust control, signal processing, spectral estimation, stochastic realization theory, and the use of the moments of a probability density. Many of these applications are also still works in progress. In this paper, we consider the generalized moment problem, expressed in terms of a basis of a finite-dimensional subspace P of the Banach space C[a, b] and a "positive" sequence c, but with a new wrinkle inspired by the applications to systems and control. We seek to parameterize solutions which are positive "rational" measures in a suitably generalized sense. Our parameterization is given in terms of smooth objects. In particular, the desired solution space arises naturally as a manifold which can be shown to be diffeomorphic to a Euclidean space and which is the domain of some canonically defined functions. The analysis of these functions, and related maps, yields interesting corollaries for the moment problem and its applications, which we compare to those in the recent literature and which play a crucial role in part of our proof.

  • 350.
    Klamroth, Kathrin
    et al.
    Institute of Applied Mathematics, University of Erlangen Nuremberg.
    Miettinen, Kaisa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Integrating Approximation and Interactive Decision Making in Multicriteria Optimization2008In: Operations Research, ISSN 0030-364X, E-ISSN 1526-5463, Vol. 56, no 1, p. 222-234Article in journal (Refereed)
    Abstract [en]

    We present a new interactive hybrid approach for solving multicriteria optimization problems where features of approximation methods and interactive approaches are incorporated. We produce rough approximations of the nondominated set and let the decision maker indicate with the help of reference points where to refine the approximation. In this way, (s)he iteratively directs the search toward the best nondominated solution. After the decision maker has identified the most interesting region of the nondominated set, the final solution can be fine-tuned with existing interactive methods. We suggest different ways of updating the reference point as well as discuss visualizations that can be used in comparing different nondominated solutions. The new method is computationally relatively inexpensive and easy to use for the decision maker.

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