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Permissive Controller Synthesis for Probabilistic Systems

Klaus Dräger‚ Vojtĕch Forejt‚ Marta Kwiatkowska‚ David Parker and Mateusz Ujma


We propose novel controller synthesis techniques for probabilistic systems modelled using stochastic two-player games: one player acts as a controller, the second represents its environment, and probability is used to capture uncertainty arising due to, for example, unreliable sensors or faulty system components. Our aim is to generate robust controllers that are resilient to unexpected system changes at runtime, and exible enough to be adapted if additional constraints need to be imposed. We develop a permissive controller synthesis framework, which generates multi-strategies for the controller, o ering a choice of control actions to take at each time step. We formalise the notion of permissiveness using penalties, which are incurred each time a possible control action is blocked by a multi-strategy. Permissive controller synthesis aims to generate a multi-strategy that minimises these penalties, whilst guaranteeing the satisfaction of a speci ed system property. We establish several key results about the optimality of multi-strategies and the complexity of synthesising them. Then, we develop methods to perform permissive controller synthesis using mixed integer linear programming and illustrate their e ectiveness on a selection of case studies.