Permissive Controller Synthesis for Probabilistic Systems

Abstract

Abstract. 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 flexible 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, offering a choice of control actions to take at each time step. We formalise the notion of permissivity using penalties, which are incurred each time a possible control action is disallowed by a multi-strategy. Permissive controller synthesis aims to generate a multi-strategy that minimises these penalties, whilst guaranteeing the satisfaction of a specified 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 effectiveness on a selection of case studies.

The 10,000 Facets of MDP Model Checking

“…Whereas MDP model checking typically generates a single policy that is optimal with respect to a given objective, recently this has been extended to obtaining multi-policies [66]. Such multi-policies specify multiple possible actions rather than a single possible action.…”

Permissive Controller Synthesis for Probabilistic Systems

“…Next, we establish several fundamental results about the permissive controller synthesis problem. Proofs can be found in [13].…”

“…For randomised multi-strategies, with some technical effort we can encode existence of the required multi-strategy as a formula of the existential fragment of the theory of real arithmetic, solvable with polynomial space [7]. See [13].…”

“…Part 2 of Theorem 6 states that, for static penalties, we can further reduce the possible multi-strategies that we need to consider. This, however, does not extend to dynamic penalties (see [13]). Lastly, we define the probabilities p 1 , .…”

Synthesis of probabilistic models for quality-of-service software engineering

“…Recent advances in PMC reinforced its applicability to the cost-effective engineering of software both at design time (Baier et al 2010;Calinescu et al 2016;Kwiatkowska et al 2010) and at runtime (Calinescu et al 2012;Draeger et al 2014). The design-time use of the technique involves the verification of alternative designs of a SUD.…”