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A Stochastic Games Framework for Verification and Control of Discrete Time Stochastic Hybrid Systems

Author(s):

J. Ding, M. Kamgarpour, S. Summers, A. Abate, J. Lygeros, C. J. Tomlin
Conference/Journal:

Automatica, vol. 49, no. 9, pp. 26652674
Abstract:

We describe a framework for analyzing probabilistic reachability and safety problems for discrete time stochastic hybrid systems within a dynamic games setting. In particular, we consider finite horizon zero-sum stochastic games in which a control has the objective of reaching a target set while avoiding an unsafe set in the hybrid state space, and a rational adversary has the opposing objective. We derive an algorithm for computing the maximal probability of achieving the control objective, subject to the worst-case adversary behavior. From this algorithm, sufficient conditions of optimality are also derived for the synthesis of optimal control policies and worst-case disturbance strategies. These results are then specialized to the safety problem, in which the control objective is to remain within a safe set. We illustrate our modeling framework and computational approach using both a tutorial example with jump Markov dynamics and a practical application in the domain of air traffic management.

Year:

2013
Type of Publication:

(01)Article
Supervisor:



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@article{Ding20132665,
title = "A stochastic games framework for verification and control of discrete time stochastic hybrid systems ",
journal = "Automatica ",
volume = "49",
number = "9",
pages = "2665 - 2674",
year = "2013",
note = "",
issn = "0005-1098",
doi = "http://dx.doi.org/10.1016/j.automatica.2013.05.025",
url = "http://www.sciencedirect.com/science/article/pii/S0005109813003087",
author = "Jerry Ding and Maryam Kamgarpour and Sean Summers and Alessandro Abate and John Lygeros and Claire Tomlin",
keywords = "Hybrid systems",
keywords = "Stochastic systems",
keywords = "Dynamic games",
keywords = "Controller synthesis",
keywords = "Reachability "
}
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