Compositional synthesis of finite abstractions for networks of systems: A small-gain approach

Swikir, Abdalla; Zamani, Majid

doi:10.1016/j.automatica.2019.06.021

Cited by 36 publications

(25 citation statements)

References 23 publications

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“…Motivated by those abstraction-based techniques in [6], [7], [8] and their limitations, this work proposes an approach to analyze approximate initial-state opacity for networks of switched systems by constructing their opacity-preserving finite abstractions compositionally. There have been some recent results proposing compositional techniques for constructing finite abstractions for networks of systems (see the results in [9], [10], [11], [12] for more details). However, the aforementioned compositional schemes are proposed for the sake of controller synthesis for temporal logic properties, and none of them are applicable to deal with security properties.…”

Section: Introductionmentioning

confidence: 99%

Compositional Verification of Initial-State Opacity for Switched Systems

Liu

Swikir

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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In this work, we propose a compositional framework for the verification of approximate initial-state opacity for networks of discrete-time switched systems. The proposed approach is based on a notion of approximate initial-state opacity-preserving simulation functions (InitSOPSFs), which characterize how close concrete networks and their finite abstractions are in terms of the satisfaction of approximate initialstate opacity. We show that such InitSOPSFs can be obtained compositionally by assuming some small-gain type conditions and composing so-called local InitSOPSFs constructed for each subsystem separately. Additionally, for switched systems satisfying certain stability property, we provide an approach to construct their finite abstractions together with the corresponding local InitSOPSFs. Finally, the effectiveness of our results is illustrated through an example.

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Section: Introductionmentioning

confidence: 99%

Compositional Verification of Initial-State Opacity for Switched Systems

Liu

Swikir

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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“…Note that (14b) could be transformed to a LMI using the Schur complement lemma (see [18,Remark 4.7]). Take the following simulation function candidates for the mentioned chosen state space:…”

Section: A Abstractions For Linear Systemsmentioning

confidence: 99%

Compositional Construction of Abstractions for Infinite Networks of Switched Systems

Sharifi

Swikir

Noroozi³

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement of the original (known as concrete) system in a controller design process. Having synthesized a controller for the abstract system, the controller is refined to a more detailed controller for the concrete system. To quantify the mismatch between the output trajectory of the approximation and of that the original system, we use the notion of socalled simulation functions. In particular, each subsystem in the concrete network and its corresponding one in the abstract network is related through a local simulation function. We show that if the local simulation functions satisfy a certain smallgain type condition developed for a network of infinitely many subsystems, then the aggregation of the individual simulation functions provides an overall simulation function between the overall abstraction and the concrete network. For a network of linear switched systems, we systematically construct local abstractions and local simulation functions, where the required conditions are expressed in terms of linear matrix inequalities and can be efficiently computed. We illustrate the effectiveness of our approach through an application to frequency control in a power gird with a switched (i.e. time-varying) topology.

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“…The authors in [16] proposed a compositional abstraction approach based on the notion of interconnection-compatible approximate bisimulation. Other approaches have been proposed recently using small-gain (or relaxed small-gain) like conditions [17], [18], [19], [20], [21] and dissipativity property [22], [23], [24]. The authors in [25], [26] presented a compositional abstraction and controller synthesis approach to the class of cascade interconnected systems.…”

Section: Introductionmentioning

confidence: 99%

Contract-Based Design of Symbolic Controllers for Safety in Distributed Multiperiodic Sampled-Data Systems

Saoud

Girard

Fribourg

2021

IEEE Trans. Automat. Contr.

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This paper presents a symbolic control approach to the design of distributed safety controllers for a class of continuous-time nonlinear systems. More precisely, we consider systems made of components where each component is equipped with a sampled-data controller with its own sampling period, resulting globally in a distributed multiperiodic sampled-data system. Moreover, controllers receive partial information on the state of the other components. We propose a component-based approach to controller synthesis, which relies on the use of abstractions and continuous-time assume-guarantee contracts. The abstractions describe the dynamics of the system from the point of view of each component based on the information structure, while assume-guarantee contracts specify guarantees that a component must satisfy if assumptions on the other components are met. We show that our approach makes it possible to decompose a global safety control problem into local ones that can be solved independently. We then show how symbolic control techniques can be used to synthesize controllers that enforce the local control objectives. Illustrative applications in building automation and vehicle platooning are shown.

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Compositional synthesis of finite abstractions for networks of systems: A small-gain approach

Cited by 36 publications

References 23 publications

Compositional Verification of Initial-State Opacity for Switched Systems

Compositional Verification of Initial-State Opacity for Switched Systems

Compositional Construction of Abstractions for Infinite Networks of Switched Systems

Contract-Based Design of Symbolic Controllers for Safety in Distributed Multiperiodic Sampled-Data Systems

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