Permissive Controller Synthesis for Probabilistic Systems

TL;DR

This paper introduces a new framework for synthesizing robust, flexible controllers for probabilistic systems modeled as stochastic two-player games, focusing on generating multi-strategies that balance control options with system property guarantees.

Contribution

It develops a permissive controller synthesis framework using penalties to formalize permissivity, and provides methods based on mixed integer linear programming for practical implementation.

Findings

Multi-strategies can be optimized to minimize penalties while ensuring system properties.

The proposed methods are effective on various case studies.

Complexity results for synthesizing optimal multi-strategies are established.

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.