Compositional construction of control barrier functions for continuous-time stochastic hybrid systems

In this work, we propose a compositional framework for the construction of control barrier functions networks continuous-time stochastic hybrid systems enforcing complex logic specifications expressed by finite-state automata. The proposed scheme is based on notion so-called pseudo-barrier computed subsystems, employing which one can synthesize controllers interconnected over finite-time horizon. Particularly, first leverage sufficient small-gain type conditions to compositionally construct corresponding subsystems. Then, using constructed functions, provide probabilistic guarantees satisfaction given in bounded time respect, decompose specification simpler reachability tasks automata representing complements original We then systematic approaches solve those computing functions. Two different techniques are provided (i) sum-of-squares (SOS) optimization program and (ii) counter-example guided inductive synthesis (CEGIS) search subsystems while synthesizing local controllers. demonstrate effectiveness our results applying them fully-interconnected Kuramoto network 100 nonlinear oscillators with Markovian switching signals.