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Static Diffusive Couplings in Heterogeneous Linear Networks *

IFAC Proceedings Volumes 2012年第26期45卷 258-263页

作者： Georg S. Seyboth Dimos V. Dimarogonas Karl H. Johansson Frank Allgöwer Institute for Systems Theory and Automatic Control University of Stuttgart Pfaffenwaldring 9 70550 Stuttgart Germany ACCESS Linnaeus Center School of Electrical Engineering Royal Institute of Technology (KTH) 100 44 Stockholm Sweden

Recently, necessary and sufficient conditions for output synchronization of linear systems via diffusive couplings have been reported. In this paper, we study the case when such conditions are not satisfied and exact synchronization is impossible. In particular, we study two kinds of heterogeneous linear networks: (i) non-identical harmonic oscillators and (ii) double-integrators. We show that static diffusive couplings render heterogeneous networks of harmonic oscillators asymptotically stable. Networks of non-identical double-integrators, in contrast, are not asymptotically stable but synchronize with bounded synchronization error depending on the network topology and the heterogeneity in the agent dynamics. Numerical examples illustrate the results.

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PARALLEL SIMULTANEOUS STABILIZATION OF A SET OF PORT-CONTROLLED HAMILTONIAN systems SUBJECT TO ACTUATOR SATURATION

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Journal of systems Science & Complexity 2011年第1期24卷 120-139页

作者： Airong WEI Yuzhen WANG Xiaoming HU School of Control Science and Engineering Shandong University Jinan 250061 ChinaOptimization and Systems Theory Royal Institute of Technology SE-10044 Stockholm Sweden School of Control Science and Engineering Shandong University Jinan 250061 China Optimization and Systems Theory Royal Institute of Technology SE-100 44 Stockholm Sweden ACCESS Linnaeus Center Royal Institute of Technology SE-100 44 Stockholm Sweden

This paper investigates parallel simultaneous stabilization （PSS） of a set of multi-input nonlinear Port-Controlled Hamiltonian （PCH） systems subject to actuator saturation （AS）, and proposes a number of results on the design of PSS controllers for the PCH systems with AS. Firstly, the case of two PCH systems with AS is studied. Exploring the special property of the saturation nonlinearity and the structural properties of dissipative Hamiltonian system, the two systems are combined to generate an augmented PCH system, with which some results on the control design are then obtained. When there are external disturbances in the two systems, a robust PSS controller is designed for the systems. Secondly, the case of more than two PCH systems with AS is investigated, and several new results are proposed for the PSS problem. Finally, two illustrative examples are presented to show that the stabilization controllers obtained in this paper work very well.

关键词： Actuator saturation PCH system robust parallel simultaneous stabilization

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Dynamic equations on time-scale: application to stability analysis and stabilization of aperiodic sampled-data systems

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IFAC Proceedings Volumes 2011年第1期44卷 11374-11379页

作者： C. Briat U.T. Jönsson ACCESS Linnaeus Centre Division of Optimization and Systems Theory Royal Institute of Technology (KTH) 100 44 Stockholm Sweden

Abstract The stability analysis of systems with aperiodic sampling is analyzed in the framework of dynamic equations on time-scales. Lyapunov theory is used, with sample-period-dependent and independent Lyapunov functions, to obtain stability conditions expressed in terms of parameter dependent matrix inequalities. The examples illustrate the efficiency of the approach which is able to recover, for some systems, the theoretical results for the periodic sampling case even in the aperiodic case. It is also shown that some systems may have admissible varying sampling periods located in disjoint sets. Finally, stabilization results via switching state-feedback are provided; both robust and sampling-period-dependent controllers are considered. It is shown that the latter ones, using the information on the sampling period, can improve stability properties. Stabilization examples illustrate the effectiveness of the approach.

关键词： Sampled-data systems dynamic equations on time-scales LMIs LPV control

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Stability criteria for asynchronous sampled-data systems - A fragmentation approach

Stability criteria for asynchronous sampled-data systems - A...

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作者： Briat, C. Seuret, A. ACCESS Linnaeus Centre Division of Optimization and Systems Theory KTH SE-10044 Stockholm Sweden GIPSA-lab. NeCS INRIA Project-Team Control Systems Department - INP Domaine Universitaire 38400 Saint Martin d'Heres France

ISBN: (纸本)9783902661937

The stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using a fragmentation technique inspired from recent advances in time-delay systems theory. The approach leads to a tractable convex feasibility problem involving a small number of finite dimensional LMIs. The approach is then finally illustrated through several examples. © 2011 IFAC.

关键词： Stability criteria

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Distributed positioning of autonomous mobile sensors with application to coverage control

Distributed positioning of autonomous mobile sensors with ap...

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作者： Dürr, Hans-Bernd Stanković, Miloš S. Johansson, Karl Henrik Institute for Systems Theory and Automatic Control University of Stuttgart Germany ACCESS Linnaeus Center School of Electrical Engineering Royal Institute of Technology 100-44 Stockholm Sweden

ISBN: (纸本)9781457700804

We consider problems in multi-agent systems where a network of mobile sensors needs to self-organize such that some global objective function is maximized. To deal with the agents' lack of global information we approach the problem in a game-theoretic framework where agents/players are only able to access local measurements of their own local utility functions whose parameters and detailed analytical forms may be unknown. We then propose a distributed and adaptive algorithm, where each agent applies a local extremum seeking feedback adopted to its specific motion dynamics, and prove its global practical stability, implying that the agents asymptotically reach a configuration that is arbitrary close to the globally optimal one. For the stability analysis we introduce a novel methodology based on a Lie bracket trajectory approximation and combine it with a potential game approach. We apply the proposed algorithm to the sensor coverage problem and solve it in a distributed way where the agents do not need any a priori knowledge about the distribution of the events to be detected and about the detection probabilities of the individual agents. The proposed scheme is illustrated through simulations. © 2011 AACC American Automatic Control Council.

关键词： Multi agent systems

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Robust stability analysis in the *-norm and Lyapunov-Razumikhin functions for the stability analysis of time-delay systems

Robust stability analysis in the *-norm and Lyapunov-Razumik...

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IEEE Conference on Decision and Control

作者： Corentin Briat ACCESS Linnaeus Centre Division of Optimization and Systems Theory KTH SE-100 44 Stockholm SWEDEN

ISBN: (纸本)9781612848006

Lyapunov-Krasovskii functionals have been shown to have connections with input-output techniques considering delay operators mapping L_(2) to L_(2). It is shown here that Lyapunov-Razumikhin functions can also be connected to the input-output framework by considering operators on L_(infinity) and the corresponding Small-Gain Theorem. Several important results from the Lyapunov-Razumikhin Theorem are retrieved and extended.

关键词： Time-delay systems Lyapunov-Razumikhin Functions Robust stability -norm

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Robust stability analysis of uncertain Linear Positive systems via Integral Linear Constraints: L_(1)- and L_(infinity)-gain characterizations

Robust stability analysis of uncertain Linear Positive Syste...

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IEEE Conference on Decision and Control

作者： Corentin Briat ACCESS Linnaeus Centre Division of Optimization and Systems Theory KTH SE-100 44 Stockholm SWEDEN

ISBN: (纸本)9781612848006

Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustness and performance analysis and lead to L_(1)- and L_(infinity)-gain characterizations. This naturally guides to the definition of Integral Linear Constraints (ILCs) for the characterization of input-output nonnegative uncertainties. It turns out that these integral linear constraints can be linked to the Laplace domain, in order to be tuned adequately, by exploiting the L_(1)-norm and input/output signals properties. This dual viewpoint allows to prove that the static-gain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive time-delay systems. The obtained stability and performance analysis conditions are expressed in terms of (robust) linear programming problems that are transformed into finite dimensional ones using the Handelman's Theorem. Several examples are provided for illustration.

关键词： Positive linear systems Integral Linear Constraints Robustness Robust linear programming

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Simple conditions for L 2 stability and stabilization of networked control systems

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IFAC Proceedings Volumes 2011年第1期44卷 96-101页

作者： Y. Ariba C. Briat K.H. Johansson ACCESS Linnaeus Centre School of Electrical Engineering Royal Institute of Technology (KTH) 100 44 Stockholm Sweden ACCESS Linnaeus Centre Division of Optimization and Systems Theory Royal Institute of Technology (KTH) 100 44 Stockholm Sweden

Abstract The stability analysis and stabilization of networked control systems subject to data loss and time-varying transmission delays are explored. The stability result is based on quadratic separation and operator theory, which allows to capture the above phenomena into the single formalism of aperiodic sampling. The obtained stability condition is expressed through an LMI. The stabilization problem is a bit more involved due to the inherent structure of the obtained LMI. An approximation (dilation) is then proposed to obtain a more tractable LMI for stabilization. Several examples illustrate the effectiveness of the proposed approach.

关键词： Networked Control systems Quadratic Separation LMIs

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Stability Criteria for Asynchronous Sampled-data systems – A Fragmentation Approach

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IFAC Proceedings Volumes 2011年第1期44卷 1313-1318页

作者： C. Briat A. Seuret ACCESS Linnaeus Centre Division of Optimization and Systems Theory KTH SE-10044 Stockholm Sweden GIPSA-lab NeCS INRIA Project-Team – Control Systems Department – INP BP 46 Domaine Universitaire – 38400 Saint Martin d'Heres – FRANCE

Abstract The stability analysis of asynchronous sampled-data systems is studied. The approach is based on a recent result which allows to study, in an equivalent way, the quadratic stability of asynchronous sampled-data systems in a continuous-time framework via the use of peculiar functionals satisfying a necessary boundary condition. The method developed here is an extension of previous results using a fragmentation technique inspired from recent advances in time-delay systems theory. The approach leads to a tractable convex feasibility problem involving a small number of finite dimensional LMIs. The approach is then finally illustrated through several examples.

关键词： asynchronous sampled-data systems robustness LMIs

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A Lie Bracket Approximation for Extremum Seeking Vehicles

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IFAC Proceedings Volumes 2011年第1期44卷 11393-11398页

作者： Miloš S Stanković Hans-Bernd Dürr Karl Henrik Johansson Institute for Systems Theory and Automatic Control University of Stuttgart Germany ACCESS Linnaeus Center School of Electrical Engineering Royal Institute of Technology (KTH) 100-44 Stockholm Sweden

Abstract In this paper we propose a novel methodology for the analysis of autonomous vehicles seeking the extremum of an arbitrary smooth nonlinear map in the plane. By interpreting the extremum seeking schemes as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we calculate a simplified system which approximates the qualitative behavior of the original one better than existing methods. By examining this approximate Lie bracket system, we are able to directly derive properties of the original one. Thus, by showing that the Lie bracket direction is directly related to the unknown gradient of the objective function we prove global uniform practical asymptotic stability of the extremum point for vehicles modeled as single integrators and non-holonomic unicycles. We illustrate the proposed method through simulations.

关键词： Extremum Seeking Autonomous Mobile Robots Stability Nonlinear Control systems

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