  In this paper, 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 based on the corresponding augmented pseudo-barrier
certificates of subsystems. Then we quantify upper bounds on exit probabilities
- the probability that an interconnected system reaches certain unsafe regions
- in a finite-time horizon using the constructed augmented barrier
certificates. 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 first to a room temperature
network containing 1000 rooms. Finally, we apply our techniques to a network of
500 switched subsystems (totally 1000 dimensions) accepting multiple barrier
certificates with a dwell-time condition, and provide upper bounds on the
probability that the interconnected system reaches some unsafe region in a
finite-time horizon.
