Formal Controller Synthesis from Specifications Given by Discrete-Time Hybrid Automata

This paper deals with formal controller synthesis for discrete-time dynamical systems. For a specification under the form of a discrete-time hybrid automaton, we aim at synthesizing controllers such that the trajectories of the closed-loop system are also trajectories of the hybrid automaton. We first 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. Then, we propose an approach based on the use of symbolic (i.e. finite-state) abstractions of both the system and the specification. Effective computations are discussed for systems that are monotone and for specifications given by piecewise affine hybrid automata. We extend our approach to handle specifications with additional safety or reachability requirements. Finally, we illustrate our approach with examples from autonomous vehicle control

Contract Based Design of Symbolic Controllers for Interconnected Multiperiodic Sampled-Data Systems

International audienceThis paper deals with the synthesis of symbolic controllers for interconnected sampled-data systems where each component has its own sampling period. A compositional approach based on continuous-time assume-guarantee contracts is used. We provide sufficient conditions guaranteeing for a sampled-data system, satisfaction of an assume-guarantee contract and completeness of trajectories. Then, compositional results can be used to reason about interconnection of mul-tiperiodic sampled-data systems. We then show how discrete abstractions and symbolic control techniques can be applied to enforce the satisfaction of contracts and ensure completeness of trajectories. Finally, theoretical results are applied to a vehicle platooning problem on a circular road, which show the effectiveness of our approach