Formal controller synthesis from specifications given by discrete-time hybrid automata

Abstract

This paper deals with formal controller synthesis for discrete-time dynamical systems. We consider a specification provided under the form of a discrete-time hybrid automaton with external inputs, which can represent, for instance, instructions or informations received from a human user or from another system. The hybrid automaton describes the intended behavior of the system and we first consider the problem of synthesizing a controller such that the maximal trajectories of the closed-loop system are also maximal trajectories of the hybrid automaton. We show that the existence of an alternating simulation relation from the specification to the open-loop system is a necessary and sufficient condition for the existence of such controllers. To be able to solve this problem using symbolic (i.e. finite-state) abstractions, we provide a method to compute a symbolic specification that under-approximates the behavior of the hybrid automata. Then, we extend our approach to consider additional safety or reachability requirements so that some unsafe (e.g. blocking) states are avoided or some target states are reached, respectively. The originality of the problem is that these additional requirements are not formulated over the states of the system but over the states of the specification. Finally, we demonstrate the effectiveness of our approach with two illustrative examples from autonomous vehicle control.