Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems

Girard, Antoine; Pola, Giordano; Tabuada, Paulo

doi:10.1007/978-3-540-78929-1_15

Cited by 112 publications

(282 citation statements)

References 12 publications

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“…Over a simulation horizon [0, T ], we select a β that is a monotonically decreasing function of time, so that β(0) = 1 and β(T ) = 0. Let us denote the solution of (11) from (x v ) 0 with x v (t, (x v ) 0 ) ∈ R 2 , t ≥ 0.…”

Section: Non-identity Metricsmentioning

confidence: 99%

“…Let us further perturb the model in (11) with a Wiener process with diffusion term α v |V 4 (x v )|. Over a simulation horizon [0, T ], we select a β that is a monotonically decreasing function of time, so that β(0) = 1 and β(T ) = 0.…”

Section: Non-identity Metricsmentioning

confidence: 99%

“…The conditions in [1] are shown to be related to a probabilistic version of the concept of incremental stability [2]. Interestingly, both the notion of Lyapunov stability and the concept of incremental stability have been recently exploited in the study of (bi-)simulation relations for deterministic models on continuous spaces [10], [11].…”

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Probabilistic bisimulations of switching and resetting diffusions

Abate

2010

49th IEEE Conference on Decision and Control (CDC)

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This contribution presents sufficient conditions for the existence of probabilistic bisimulations between two diffusion processes that are additionally endowed with switching and resetting behaviors. A probabilistic bisimulation between two stochastic processes is defined by means of a bisimulation function, which induces an approximation metric over the distance between the two processes. The validity of the proposed sufficient conditions results in the explicit characterization of one such bisimulation function. The conditions depend on contractivity properties of the two stochastic processes.

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Section: Non-identity Metricsmentioning

confidence: 99%

Section: Non-identity Metricsmentioning

confidence: 99%

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Probabilistic bisimulations of switching and resetting diffusions

Abate

2010

49th IEEE Conference on Decision and Control (CDC)

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“…For example, controllable linear control systems and incrementally stable nonlinear control systems were shown in [2] and respectively in [4], [5], to admit symbolic models. Symbolic models for multi-affine systems have been proposed in the work of [6] and for nonlinear switched systems in the work of [7]. One challenge in this research line is to enlarge the class of systems admitting symbolic models.…”

Section: Introductionmentioning

confidence: 99%

Alternating approximately bisimilar symbolic models for nonlinear control systems with unknown time-varying delays

Pola

Pepe

Benedetto

2010

49th IEEE Conference on Decision and Control (CDC)

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In this paper we study existence of symbolic models for the class of nonlinear control systems with unknown time-varying delays. We first introduce the notion of incrementally input-delay-to-state stability and characterize it by means of Liapunov-Krasovskii functionals. We then derive sufficient conditions that guarantee existence of symbolic models which are approximately equivalent, in the sense of alternating approximate bisimulation, to the original time-delay system. keywords: Time-delay systems, symbolic models, alternating approximate bisimulation, incremental input-delayto-state stability, time-varying delays.

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“…Some of these classes include Timed automata [2], O-minimal hybrid automata [20], [4] and STORMED hybrid systems [25]. More recently, approximate notions of simulation and bisimulation have been proposed [10], [9] and used in the analysis of reachability and safety properties [11], [22].…”

Section: Introductionmentioning

confidence: 99%

Foundations for approximation based analysis of stability properties of hybrid systems

Prabhakar

2012

2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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We discuss pre-orders for reasoning about stability properties of hybrid systems, including Lyapunov stability, asymptotic stability, input-to-state stability and incremental input-to-state stability. We strengthen the classical notion of equivalence between processes, namely, bisimulation with continuity and uniformity conditions and show that the new notions preserve the stability properties for hybrid systems. We demonstrate the usefulness of our results by casting various classical methods for proving stability as constructing simpler systems which are related to the original systems by uniformly continuous notions of pre-orders and proving the simpler systems to be stable.

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Approximately Bisimilar Symbolic Models for Incrementally Stable Switched Systems

Cited by 112 publications

References 12 publications

Probabilistic bisimulations of switching and resetting diffusions

Probabilistic bisimulations of switching and resetting diffusions

Alternating approximately bisimilar symbolic models for nonlinear control systems with unknown time-varying delays

Foundations for approximation based analysis of stability properties of hybrid systems

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