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  • 1.
    Agram, Nacira
    et al.
    Linnaeus Univ LNU, Dept Math, Växjö, Sweden..
    Djehiche, Boualem
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    On a class of reflected backward stochastic Volterra integral equations and related time-inconsistent optimal stopping problems2021In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 155, p. 104989-, article id 104989Article in journal (Refereed)
    Abstract [en]

    We introduce a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We prove existence and uniqueness by a fixed point argument and derive a comparison result. Moreover, we show how the solution of our problem is related to a time-inconsistent optimal stopping problem and derive an optimal strategy.

  • 2.
    Agram, Nacira
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hu, Yaozhong
    Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada..
    oksendal, Bernt
    Univ Oslo, Dept Math, POB 1053, N-0316 Oslo, Norway..
    Mean-field backward stochastic differential equations and applications2022In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 162, article id 105196Article in journal (Refereed)
    Abstract [en]

    In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of the form & nbsp;& nbsp;{dY(t) = -[alpha(1)(t)Y(t) +& nbsp;beta(1)(t)Z(t) +& nbsp;integral(R0 & nbsp;)eta(1)(t,& nbsp;zeta)K(t,& nbsp;zeta)nu(d zeta) +& nbsp;alpha(2)(t)E[Y(t)] +& nbsp;beta(2)(t)E[Z(t)] +& nbsp;integral(R0 & nbsp;)eta(2)(t,& nbsp;zeta)E[K(t,& nbsp;zeta)]nu(d zeta) +& nbsp;gamma(t)]dt + Z(t)dB(t) +& nbsp;integral K-R0 (t,& nbsp;zeta)(N) over tilde(dt, d zeta), t & nbsp;is an element of & nbsp;[0, T].Y(T) =xi.& nbsp;& nbsp;where (Y, Z, K) is the unknown solution triplet, B is a Brownian motion, (N) over tilde is a compensated Poisson random measure, independent of B. We prove the existence and uniqueness of the solution triplet (Y, Z, K) of such systems. Then we give an explicit formula for the first component Y(t) by using partial Malliavin derivatives. To illustrate our result we apply them to study a mean-field recursive utility optimization problem in finance.

  • 3.
    Agram, Nacira
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Øksendal, Bernt
    Department of Mathematics, University of Oslo, Norway.
    Optimal stopping of conditional McKean–Vlasov jump diffusions2024In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 188, article id 105815Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is to study the optimal stopping problem of conditional McKean–Vlasov (mean-field) stochastic differential equations with jumps (conditional McKean–Vlasov jump diffusions, for short). We obtain sufficient variational inequalities for a function to be the value function of such a problem and for a stopping time to be optimal.

    The key is that we combine the conditional McKean–Vlasov equation with the associated stochastic Fokker–Planck partial integro-differential equation for the conditional law of the state. This leads to a Markovian system which can be handled by using a version of a Dynkin formula.

    Our verification result is illustrated by finding the optimal time to sell in a market with common noise and jumps.

  • 4.
    Andersson, Daniel
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    The relaxed general maximum principle for singular optimal control of diffusions2009In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, ISSN 01676911, Vol. 58, no 1, p. 76-82Article in journal (Refereed)
    Abstract [en]

    In this paper we study optimality in stochastic control problems where the state process is a stochastic differential equation (SDE) and the control variable has two components, the first being absolutely continuous and the second singular. A control is defined as a solution to the corresponding martingale problem. To obtain existence of an optimal control Haussmann and Suo [U.G. Haussmann, W. Suo, Singular optimal stochastic controls I: Existence, SIAM J. Control Optim. 33 (3) (1995) 916-936] relaxed the martingale problem by extending the absolutely continuous control to the space of probability measures on the control set. Bahlali et al. [S. Bahlali, B. Djehiche, B. Mezerdi, The relaxed stochastic maximum principle in singular optimal control of diffusions, SIAM J. Control Optim. 46 (2) (2007) 427-444] established a maximum principle for relaxed singular control problems with uncontrolled diffusion coefficient. The main goal of this paper is to extend their results to the case where the control enters the diffusion coefficient. The proof is based on necessary conditions for near optimality of a sequence of ordinary controls which approximate the optimal relaxed control. The necessary conditions for near optimality are obtained by Ekeland's variational principle and the general maximum principle for (strict) singular control problems obtained in Bahlali and Mezerdi [S. Bahlali, B. Mezerdi, A general stochastic maximum principle for singular control problems, Electron J. Probab. 10 (2005) 988-1004. Paper no 30]. © 2008 Elsevier B.V. All rights reserved.

  • 5.
    Barreau, Matthieu
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Tarbouriech, Sophie
    Univ Toulouse, CNRS, LAAS, UPS, Toulouse, France..
    Gouaisbaut, Frederic
    Univ Toulouse, CNRS, LAAS, UPS, Toulouse, France..
    Lyapunov stability analysis of a mass-spring system subject to friction2021In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 150, article id 104910Article in journal (Refereed)
    Abstract [en]

    This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically stick to the ground. The objective consists of developing numerically tractable conditions ensuring the global asymptotic stability of the unique equilibrium point. The proposed approach merges two intermediate results: The first one relies on the characterization of an attractor around the origin, to which converges the closed-loop trajectories. The second result assesses the regional asymptotic stability of the equilibrium point by estimating its basin of attraction. The main result relies on conditions allowing to ensure that the attractor issued from the first result is included in the basin of attraction of the origin computed from the second result. An illustrative example draws the interest of the approach.

  • 6.
    Basiri, Meysam
    et al.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Bishop, Adrian N.
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Jensfelt, Patric
    KTH, School of Computer Science and Communication (CSC), Centres, Centre for Autonomous Systems, CAS.
    Distributed control of triangular formations with angle-only constraints2010In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 59, no 2, p. 147-154Article in journal (Refereed)
    Abstract [en]

    This paper considers the coupled, bearing-only formation control of three mobile agents moving in the plane. Each agent has only local inter-agent bearing knowledge and is required to maintain a specified angular separation relative to both neighbor agents. Assuming that the desired angular separation of each agent relative to the group is feasible, a triangle is generated. The control law is distributed and accordingly each agent can determine their own control law using only the locally measured bearings. A convergence result is established in this paper which guarantees global asymptotic convergence of the formation to the desired formation shape.

  • 7.
    Blomqvist, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Nagamune, R.
    Optimization-based computation of analytic interpolants of bounded complexity2005In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 54, no 9, p. 855-864Article in journal (Refereed)
    Abstract [en]

    This paper provides a unifying algorithm for computing any analytic interpolant of bounded complexity. Such computation can be performed by solving an optimization problem, due to a theorem by Georgiou and Lindquist. This optimization problem is numerically solvable by a continuation method. The proposed numerical algorithm is useful, among other cases, for designing a low-degree controller for a benchmark problem in robust control. The algorithm unifies previously developed 19 algorithms for the Caratheodory extension and the Nevanlinna-Pick interpolation to one for more general interpolation problems.

  • 8.
    Briat, Corentin
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Sename, O.
    GIPSA-Lab, Department of Control Systems (Former LAG), Grenoble Universités.
    Lafay, J. F.
    IRCCyN - Centrale de Nantes.
    Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays2010In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 59, no 8, p. 451-459Article in journal (Refereed)
    Abstract [en]

    The stabilization of uncertain LTI/LPV time-delay systems with time-varying delays by state-feedback controllers is addressed. Compared to other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow us to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the H-infinity performance measure is considered. The interest of the approach is finally illustrated through several examples.

  • 9.
    Dimarogonas, Dimos V.
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Tsiotras, P.
    Kyriakopoulos, K. J.
    Leader-follower cooperative attitude control of multiple rigid bodies2009In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 58, no 6, p. 429-435Article in journal (Refereed)
    Abstract [en]

    In this paper we extend our previous results on coordinated control of rotating rigid bodies to the case of teams with heterogeneous agents. We assume that only a certain subgroup of the agents (the leaders) is vested with the main control objective, that is, maintain constant relative orientation amongst themselves. The other members of the team must meet relaxed control specifications, namely, maintain their respective orientations within certain bounds, dictated by the orientation of the leaders. The proposed control laws respect the limited information each rigid body has with respect to the rest of its peers (leaders or followers), as well as with the rest of the team. Each rigid body is equipped with a feedback control law that utilizes the Laplacian matrix of the associated communication graph, and which encodes the limited communication capabilities between the team members. Similarly to the single integrator case, the convergence of the system relies on the connectivity of the communication graph.

  • 10.
    Farokhi, Farhad
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. 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.
    Adaptive control design under structured model information limitation: A cost-biased maximum-likelihood approach2015In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 75, p. 8-13Article in journal (Refereed)
    Abstract [en]

    Networked control strategies based on limited information about the plant model usually result in worse closed-loop performance than optimal centralized control with full plant model information. Recently, this fact has been established by utilizing the concept of competitive ratio, which is defined as the worst-case ratio of the cost of a control design with limited model information to the cost of the optimal control design with full model information. We show that an adaptive controller, inspired by a controller proposed by Campi and Kumar, with limited plant model information, asymptotically achieves the closed-loop performance of the optimal centralized controller with full model information for almost any plant. Therefore, there exists, at least, one adaptive control design strategy with limited plant model information that can achieve a competitive ratio equal to one. The plant model considered in the paper belongs to a compact set of stochastic linear time-invariant systems and the closed-loop performance measure is the ergodic mean of a quadratic function of the state and control input.

  • 11.
    Hu, Xiaoming
    KTH, Superseded Departments (pre-2005), Mathematics.
    Nonlinear state estimation for rigid-body motion with low-pass sensors2000In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 40, no 3, p. 183-190Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider the state estimation problem for the nonlinear kinematic equations of a rigid body observed under low-pass sensors. The problem is motivated from a walking robot application where inclinometers and gyros are the sensors used. We show that a non-local high gain observer exists for the nonlinear rigid-body kinematic equations and that it under a small angle assumption is possible to use one inclinometer only to estimate two angles.

  • 12.
    Huang, Lirong
    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.
    Recursive estimators with Markovian jumps2012In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 61, no 10, p. 1009-1016Article in journal (Refereed)
    Abstract [en]

    Recursive stochastic algorithms have various applications. In the literature, it is assumed that the true value lies in a connected domain. But, in many cases, it is known that the true value is contained in the union of a finite number of pairwise disjoint sets instead of a connected domain. In these situations, the existing algorithms may be not applicable. To cope with this problem, this paper proposes recursive stochastic algorithms with (event-triggered) Markovian jumps and presents sufficient conditions for almost sure convergence of the proposed algorithms. As an example of applications, this paper significantly improves an existing adaptive algorithm with the proposed method for consistent estimation of non-minimum phase zeros.

  • 13. Huang, Lirong
    et al.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Koeppl, Heinz
    Almost sure stability and stabilization of discrete-time stochastic systems2015In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 82, p. 26-32Article in journal (Refereed)
    Abstract [en]

    As is well known, noise may play a stabilizing or destabilizing role in continuous-time systems. But, for analysis and design of discrete-time systems, noise is treated as disturbance in the literature. This paper studies almost sure stability of general n-dimensional nonlinear time-varying discrete-time stochastic systems and presents a criterion based on a numerical result derived from Higham (2001), which exploits the stabilizing role of noise in discrete-time systems. As an application of the established results, this paper proposes a novel controller design method for almost sure-stabilization of linear discrete-time stochastic systems. The effectiveness of the proposed design method is verified with an example (an aircraft model subject to state-dependent noise), to which the existing results do not apply.

  • 14.
    Johansson, Karl Henrik
    et al.
    University of California, Berkeley.
    Egerstedt, Magnus
    KTH.
    Lygeros, J.
    University of California, Berkeley.
    Sastry, S.
    University of California, Berkeley.
    On the regularization of Zeno hybrid automata1999In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 38, no 3, p. 141-150Article in journal (Refereed)
    Abstract [en]

    Fundamental properties of hybrid automata, such as existence and uniqueness of executions, are studied. Particular attention is devoted to Zeno hybrid automata, which are hybrid automata that take infinitely many discrete transitions in finite time. It is shown that regularization techniques can be used to extend the Zeno executions of these automata to times beyond the Zeno time. Different types of regularization may, however, lead to different extensions. A water tank control problem and a bouncing ball system are used to illustrate the results.

    Download full text (pdf)
    zeno_scl99
  • 15.
    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.

  • 16.
    Lee, Jin Gyu
    et al.
    Univ Cambridge, Dept Engn, Control Grp, Cambridge, England..
    Kim, Junsoo
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Mixed analog-digital method of designing a heterogeneous network with the desired collective behavior and rapid convergence2022In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 160, article id 105126Article in journal (Refereed)
    Abstract [en]

    Among many advances given by the diffusive coupling on the synchronization problem, recently a design method for a continuous-time heterogeneous network with the desired collective behavior has been developed. Meanwhile, by its use of high-gain, implementation issues arise in discrete -time frameworks. The goal of this paper is thus to introduce a simple scheme that follows the philosophy of Carver Mead, a pioneer of VLSI (Very Large Scale Integration) technology, that removes those implementation issues. In the end, we utilize what corresponds to derivative consensus in continuous-time, which can be realized by, for instance, an analog electric circuit. This provides a mixed analog-digital method of designing a heterogeneous network with the desired collective behavior and rapid convergence.

  • 17.
    Liu, Kun
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Fridman, Emiila
    Tel Aviv University.
    Delay-dependent methods and the first delay interval2014In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 64, no 1, p. 57-63Article in journal (Refereed)
    Abstract [en]

    This paper deals with the solution bounds for time-delay systems via delay-dependent Lyapunov-Krasovskii methods. Solution bounds are widely used for systems with input saturation caused by actuator saturation or by the quantizers with saturation. We show that an additional bound for solutions is needed for the first time-interval, where t<τ(t), both in the continuous and in the discrete time. This first time-interval does not influence on the stability and the exponential decay rate analysis. The analysis of the first time-interval is important for nonlinear systems, e.g., for finding the domain of attraction. Regional stabilization of a linear (probably, uncertain) system with unknown and bounded input delay under actuator saturation is revisited, where the saturation avoidance approach is used.

    Download full text (pdf)
    KunLiuSCL13
  • 18.
    Lou, Youcheng
    et al.
    Chinese Academy of Sciences, Beijing, China .
    Shi, Guodong
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hong, Y.
    Convergence of random sleep algorithms for optimal consensus2013In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 62, no 12, p. 1196-1202Article in journal (Refereed)
    Abstract [en]

    In this paper, we propose a random sleep algorithm for a network to cooperatively find a point within the intersection of some convex sets, each of which is known only to a particular node. At each step, each node first chooses to project its own set or not at random by a Bernoulli decision independently. When a node has chosen to project its set, we assume that it can detect only the projection direction rather than the exact projection point, based on which the node obtains an estimate for the projection point. Then the agents update their states by averaging the estimates with their neighbors. Under directed and time-varying communication graph, sufficient and/or necessary stepsize conditions are presented for the considered algorithm converging to a consensus within the intersection set.

  • 19. Markdahl, Johan
    et al.
    Hoppe, Jens
    Wang, Lin
    Hu, Xiaoming
    A Geodesic Feedback Law to Decouple the Full and Reduced AitudeIn: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956Article in journal (Refereed)
  • 20. Markdahl, Johan
    et al.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Wang, Lin
    Hu, Xiaoming
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    A geodesic feedback law to decouple the full and reduced attitude2017In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 102, p. 32-41Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel approach to the problem of almost global attitude stabilization. The reduced attitude is steered along a geodesic path on the n - 1-sphere. Meanwhile, the full attitude is stabilized on SO(n). This action, essentially two maneuvers in sequel, is fused into one smooth motion. Our algorithm is useful in applications where stabilization of the reduced attitude takes precedence over stabilization of the full attitude. A two parameter feedback gain affords further trade-offs between the full and reduced attitude convergence speed. The closed loop kinematics on SO(3) are solved for the states as functions of time and the initial conditions, providing precise knowledge of the transient dynamics. The exact solutions also help us to characterize the asymptotic behavior of the system such as establishing the region of attraction by straightforward evaluation of limits. The geometric flavor of these ideas is illustrated by a numerical example.

  • 21.
    Markdahl, Johan
    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.
    Wenjun, Song
    Global and Invariant Aspects of Consensus on the n-SphereIn: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956Article in journal (Refereed)
  • 22.
    Ren, Wei
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Xiong, J.
    Department of Automation, University of Science and Technology of China, Hefei, 230026, China.
    Stability analysis for stochastic impulsive switched time-delay systems with asynchronous impulses and switches2019In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 133, article id 104516Article in journal (Refereed)
    Abstract [en]

    This paper studies stability of a general class of impulsive switched systems under time delays and random disturbances using multiple Lyapunov functions and average dwell-time. In the studied system, impulses and switches are allowed to occur asynchronously. As a result, the switching may occur in impulsive intervals and the impulses could also occur in switching intervals, which affect system stability greatly. Although the switches do no bring about the change of system state, multiple Lyapunov functions do not decrease at the switching times. Therefore, we study two cases: the stable continuous dynamics case and the stable impulsive dynamics case. Based on multiple Lyapunov functions and average dwell-time condition, sufficient stability conditions are derived. Finally, the obtained results are demonstrated through a numerical example from complex switched networks.

  • 23.
    Sandberg, Henrik
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hägg, Per
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Approximative model reconstruction of cascade systems2014In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 69, no 1, p. 90-97Article in journal (Refereed)
    Abstract [en]

    This letter considers how to approximately reconstruct a cascade system from a given unstructured system estimate. Many system identification methods, including subspace methods, provide reliable but generally unstructured black-box models. The problem we consider is how to find cascade systems that are close to such black-box models. For this, we use model matching techniques and optimal weighted Hankel-norm approximation to obtain accurate low-order cascade systems. We show that it is possible to bound the reconstruction error in terms of an error tolerance parameter and weighted Hankel singular values. The suggested methods are illustrated on both a numerical example and a real double tank system with experimental data.

    Download full text (pdf)
    fulltext
  • 24.
    Tegling, Emma
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Sandberg, Henrik
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Noise-induced limitations to the scalability of distributed integral control2019In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 130, p. 23-31Article in journal (Refereed)
    Abstract [en]

    We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise's impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this may in practice imply that very large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.

  • 25.
    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).

  • 26. Yang, Y.
    et al.
    Dimarogonas, Dimos V.
    KTH, School of Electrical Engineering and Computer Science (EECS), Intelligent systems, Decision and Control Systems (Automatic Control).
    Hu, X.
    Opinion consensus under external influences2018In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 119, p. 23-30Article in journal (Refereed)
    Abstract [en]

    As a means to regulate the continuous-time bounded confidence opinion dynamics, an exo-system to the original Hegselmann–Krause model is added. Some analysis is made about the properties of the combined system. Two theorems are provided in this article in terms of sufficient conditions of the exo-system that can guarantee opinion consensus for any initial conditions. Two more corollaries are given to describe the resulting synchronized opinions. 

  • 27. Zaidi, A. A.
    et al.
    Yüksel, S.
    Oechtering, Tobias
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the tightness of linear policies for stabilization of linear systems over Gaussian networks2016In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 88, p. 32-38Article in journal (Refereed)
    Abstract [en]

    In this paper, we consider stabilization of multi-dimensional linear systems driven by Gaussian noise controlled over parallel Gaussian channels. For such systems, it has been recognized that for stabilization in the sense of asymptotic stationarity or stability in probability, Shannon capacity of a channel is an appropriate measure on characterizing whether a system can be made stable when controlled over the channel. However, this is in general not the case for quadratic stabilization. On a related problem of joint-source channel coding, in the information theory literature, the source-channel matching principle has been shown to lead to optimality of uncoded or analog transmission and when such matching conditions occur, it has been shown that capacity is also a relevant figure of merit for quadratic stabilization. A special case of this result is applicable to a scalar LQG system controlled over a scalar Gaussian channel. In this paper, we show that even in the absence of source-channel matching, to achieve quadratic stability, it may suffice that information capacity (in Shannon’s sense) is greater than the sum of the logarithm of unstable eigenvalue magnitudes. In particular, we show that periodic linear time varying coding policies are optimal in the sense of obtaining a finite second moment for the state of the system with minimum transmit power requirements for a large class of vector Gaussian channels. Our findings also extend the literature which has considered noise-free systems.

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