Compositional Construction of Control Barrier Certificates for Large-Scale Stochastic Switched Systems

Abstract

In this letter, we propose a compositional framework for the construction of control barrier certificates for large-scale stochastic switched systems accepting multiple control barrier certificates with some dwell-time conditions. The proposed scheme is based on a notion of so-called augmented pseudo-barrier certificates computed for each switched subsystem, using which one can compositionally synthesize state-feedback controllers for interconnected systems enforcing safety specifications over a finite-time horizon. In particular, we first leverage sufficient max-type small-gain conditions to compositionally construct augmented control barrier certificates for interconnected systems. We the quantify upper bounds on exit probabilities - the probability that an interconnected system reaches certain unsafe regions - in a finite-time horizon. We employ a technique based on a counter-example guided inductive synthesis (CEGIS) approach to search for control barrier certificates of each mode while synthesizing safety controllers providing switching signals. We demonstrate our proposed results by applying them to two different case studies.