Decentralized Control of Infinite Systems

Abstract

We propose algorithms for the synthesis of decentralized statefeedback controllers with partial observation of infinite state systems, which are modeled by Symbolic Transition Systems. We first consider the computation of safe controllers ensuring the avoidance of a set of forbidden states and then extend this result to the deadlock free case. The termination of the algorithms solving these problems is ensured by the use of abstract interpretation techniques, but at the price of overapproximations, in particular, in the computation of the states which must be avoided. We then extend our algorithms to the case where the system to be controlled is given by a collection of subsystems (modules). This structure is exploited to locally compute a controller for each module. Our tool SMACS gives an empirical evaluation of our methods by showing their feasibility, usability and efficiency.

Towards decentralized and parameterized supervisor synthesis

“…The synthesis problems for some classes of parameterized systems have been previously studied in [64], [65]. There are also several works that directly address the problem of supervisor synthesis for a general class of infinite state systems, that are based on predicates and predicate transformers [66], [67], [68], [69], [70]. Although deadlock avoidance techniques have been well studied, the problem of enforcing livelock freedom for the closed-loop system has not been addressed in these works.…”