Supervisory Control of Infinite Symbolic Systems using Abstract Interpretation

Gall, Tristan Le; Jeannet, Bertrand; Marchand, Hervé

doi:10.1109/cdc.2005.1582126

Cited by 30 publications

(30 citation statements)

References 18 publications

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“…For example, Pre T δ (B) is given by the set of states ν which satisfy the predicate transformer ∃ν ∈ B : (ν ∈ G δ ) ∧ (ν = A δ (ν)). Further details can be found in Le Gall et al (2005); Jeannet et al (2005).…”

Section: Remarkmentioning

confidence: 99%

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Decentralized Control of Infinite Systems

Kalyon

Gall

Marchand

et al. 2011

Discrete Event Dyn Syst

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We propose algorithms for the synthesis of decentralized statefeedback controllers with partial observation of infinite state systems, which are modeled by Symbolic Transition Systems. We first consider the computation of safe controllers ensuring the avoidance of a set of forbidden states and then extend this result to the deadlock free case. The termination of the algorithms solving these problems is ensured by the use of abstract interpretation techniques, but at the price of overapproximations, in particular, in the computation of the states which must be avoided. We then extend our algorithms to the case where the system to be controlled is given by a collection of subsystems (modules). This structure is exploited to locally compute a controller for each module. Our tool SMACS gives an empirical evaluation of our methods by showing their feasibility, usability and efficiency.

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Section: Remarkmentioning

confidence: 99%

“…They also show that the problem can be solved for the particular case of Petri nets when the set of forbidden states is upward closed. Le Gall et al (2005) use symbolic techniques to control, in a centralized framework, infinite systems modeled by STS. They also use abstract interpretation techniques (e.g.…”

Section: Introductionmentioning

confidence: 99%

Decentralized Control of Infinite Systems

Kalyon

Gall

Marchand

et al. 2011

Discrete Event Dyn Syst

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“…These methods have been extended by Kalyon et al (2009) to take into account partial observation; the masks used are partitions of the state space. Le Gall et al (2005); Kalyon et al (2009) consider memoryless controller where the control decision is only based on the current state of the system.…”

Section: Introductionmentioning

confidence: 99%

“…They also show that the problem can be solved in the case of Petri nets, when the set Bad is upward-closed. Le Gall et al (2005) use, symbolic techniques to control infinite systems modelled by STS 3 . Abstract interpretation techniques as defined by Cousot and Cousot (1977) are then used by Le Gall et al (2005) to ensure that the controlled system can be effectively computed.…”

Section: Introductionmentioning

confidence: 99%

“…Le Gall et al (2005) use, symbolic techniques to control infinite systems modelled by STS 3 . Abstract interpretation techniques as defined by Cousot and Cousot (1977) are then used by Le Gall et al (2005) to ensure that the controlled system can be effectively computed. These methods have been extended by Kalyon et al (2009) to take into account partial observation; the masks used are partitions of the state space.…”

Section: Introductionmentioning

confidence: 99%

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Symbolic Supervisory Control of Infinite Transition Systems Under Partial Observation Using Abstract Interpretation

Kalyon

Gall

Marchand

et al. 2011

Discrete Event Dyn Syst

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We propose algorithms for the synthesis of state-feedback controllers with partial observation of infinite state discrete event systems modelled by Symbolic Transition Systems. We provide models of safe memoryless controllers both for potentially deadlocking and deadlock free controlled systems. The termination of the algorithms solving these problems is ensured using abstract interpretation techniques which provide an overapproximation of the transitions to disable. We then extend our algorithms to controllers with memory and to online controllers. We also propose improvements in the synthesis of controllers in the finite case which, to our knowledge, provide more permissive solutions than what was previously proposed in the literature. Our tool SMACS gives an empirical validation of our methods by showing their feasibility, usability and efficiency.

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Concurrent Games on VASS with Inhibition

Bérard

Haddad

Sassolas

et al. 2012

Lecture Notes in Computer Science

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Abstract. We propose to study concurrent games on a new extension of Vector Addition Systems with States, where inhibition conditions are added for modeling purposes. Games are a well-suited framework to solve control problems, and concurrent semantics reflect realistic situations where the environment can always produce a move before the controller, although it is never required to do so. This is in contrast with previous works, which focused mainly on turn-based semantics. Moreover, we consider asymmetric games, where environment and controller do not have the same capabilities, although they both have restricted power. In this setting, we investigate reachability and safety objectives, which are not dual to each other anymore, and we prove that (i) reachability games are undecidable for finite targets, (ii) they are 2-EXPTIME-complete for upward-closed targets and (iii) safety games are co-NP-complete for finite, upward-closed and semi-linear targets. Moreover, for the decidable cases, we build a finite representation of the corresponding controllers.

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Supervisory Control of Infinite Symbolic Systems using Abstract Interpretation

Cited by 30 publications

References 18 publications

Decentralized Control of Infinite Systems

Decentralized Control of Infinite Systems

Symbolic Supervisory Control of Infinite Transition Systems Under Partial Observation Using Abstract Interpretation

Concurrent Games on VASS with Inhibition

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