A stochastic games framework for verification and control of discrete time stochastic hybrid systems

Ding, Jerry; Kamgarpour, Maryam; Summers, Sean; Abate, Alessandro; Lygeros, John; Tomlin, Claire J.

doi:10.1016/j.automatica.2013.05.025

Cited by 46 publications

(45 citation statements)

References 28 publications

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“…The following results adapts Theorem 1 of [18] to the case of temporal logic formula satisfaction over a finite time-horizon. Theorem 1.…”

Section: Dynamic Programming For Sa F E − Ltl F Satisfactionmentioning

confidence: 74%

“…In this section, we present a dynamic programming approach to determine a solution to Problem 1. Our analysis is motivated by the treatment in [18] and [50]. We then introduce the notion of secure control barrier certificates (S-CBCs), and use these to provide a lower bound on the probability of satisfaction of the sa f e − LTL F formula φ for a defender policy under any adversary policy in terms of the accepting runs of length less than or equal to the length of the time-horizon of interest of a DFA associated with φ.…”

Section: Solution Approachmentioning

confidence: 99%

“…The result follows by an induction argument which uses the fact that T µ (d) k ,µ (a) k is a monotonic operator. We refer to [18] for details. Further, this procedure also guarantees the existence of a defender policy that will maximize the probability of satisfaction of φ under any adversary policy.…”

Section: Dynamic Programming For Sa F E − Ltl F Satisfactionmentioning

confidence: 99%

See 2 more Smart Citations

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Ramasubramanian

Niu

Clark

et al. 2019

Lecture Notes in Computer Science

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This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in sa f e − LTL F , a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discretetime dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximizes the probability of satisfaction of a sa f e − LTL F formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach.

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“…The following results adapts Theorem 1 of [18] to the case of temporal logic formula satisfaction over a finite time-horizon. Theorem 1.…”

Section: Dynamic Programming For Sa F E − Ltl F Satisfactionmentioning

confidence: 74%

Section: Solution Approachmentioning

confidence: 99%

Section: Dynamic Programming For Sa F E − Ltl F Satisfactionmentioning

confidence: 99%

See 1 more Smart Citation

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Ramasubramanian

Niu

Clark

et al. 2019

Lecture Notes in Computer Science

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“…Latest results include the use of model checking techniques in control of deterministic systems [4], games for controlling non-deterministic systems [5], linear programming and value iteration for controlling Markov decision processes [1], [6]. Through the use of abstractions, such techniques have also been used for infinite systems [7]- [12]. Alternatively, one can construct a discrete model using, e.g., [13]- [16], to which the above synthesis methods can be applied.…”

Section: Introductionmentioning

confidence: 99%

Optimal Temporal Logic Control for Deterministic Transition Systems With Probabilistic Penalties

Svoreňová

Černá

Belta

2015

IEEE Trans. Automat. Contr.

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We consider an optimal control problem for a weighted deterministic transition system required to satisfy a constraint expressed as a Linear Temporal Logic (LTL) formula over its labels. By assuming that the executions of the system incur time-varying penalties modeled as Markov chains, our goal is to minimize the expected average cumulative penalty incurred between consecutive satisfactions of a desired property. Using concepts from theoretical computer science, we provide two solutions to this problem. First, we derive a provably correct optimal strategy within the class of strategies that do not exploit values of penalties sensed in real time. Second, we show that by taking advantage of locally sensing the penalties, we can construct heuristic strategies leading to lower collected penalty. While still ensuring satisfaction of the LTL constraint, we cannot guarantee optimality in the latter case. We provide a user-friendly implementation of the proposed algorithms and analysis of two case studies.

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“…Existing computational results for reachability analysis of fully observable SHS often rely on dynamic programming formulations that require a discretization of the continuous space [2], [19], [6], [1], [18], or an approximate abstraction of the original model to an equivalent system that has the same properties [7], [22].…”

Section: Introductionmentioning

confidence: 99%

Finite state approximation for verification of partially observable stochastic hybrid systems

Lesser

Oishi

2015

Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

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We consider the problem of verification of safety specifications for stochastic hybrid systems with a controller that has access to partial observations of the state. We address this problem through a finite state approximation of the stochastic hybrid system, which enables the use of existing solution techniques for partially observable Markov decision processes. First, we review a dynamic programming formulation of the safety (viability) problem over an equivalent information state. We then solve a dynamic program over the finite state approximation to generate a lower bound to the viability probability, using a point-based method that generates samples of the information state. Our approach produces approximate probabilistic viable sets and synthesizes a controller to satisfy safety specifications. We provide error bounds and convergence results, assuming additive Gaussian noise in the continuous state dynamics and observations. Finally, we demonstrate performance of the approximation on a simple temperature regulation problem.

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A stochastic games framework for verification and control of discrete time stochastic hybrid systems

Cited by 46 publications

References 28 publications

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

Optimal Temporal Logic Control for Deterministic Transition Systems With Probabilistic Penalties

Finite state approximation for verification of partially observable stochastic hybrid systems

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