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Secure Control in Partially Observable Environments to Satisfy LTL Specifications

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Document pages: 15 pages

Abstract: This paper studies the synthesis of control policies for an agent that has tosatisfy a temporal logic specification in a partially observable environment,in the presence of an adversary. The interaction of the agent (defender) withthe adversary is modeled as a partially observable stochastic game. The goal isto generate a defender policy to maximize satisfaction of a given temporallogic specification under any adversary policy. The search for policies islimited to the space of finite state controllers, which leads to a tractableapproach to determine policies. We relate the satisfaction of the specificationto reaching (a subset of) recurrent states of a Markov chain. We present analgorithm to determine a set of defender and adversary finite state controllersof fixed sizes that will satisfy the temporal logic specification, and provethat it is sound. We then propose a value-iteration algorithm to maximize theprobability of satisfying the temporal logic specification under finite statecontrollers of fixed sizes. Lastly, we extend this setting to the scenariowhere the size of the finite state controller of the defender can be increasedto improve the satisfaction probability. We illustrate our approach with anexample.

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