Safety Barrier Certificates for Stochastic Control Systems with Wireless Communication Networks

This work is concerned with a formal approach for safety controller synthesis of stochastic control systems with both process and measurement noises while considering wireless communication networks between sensors, controllers, and actuators. The proposed scheme is based on control barrier certificates (CBC), which allows us to provide safety certificates for wirelessly-connected stochastic control systems. Despite the existing literature on designing control barrier certificates, there has been no consideration of wireless communication networks to capture potential packet losses, which is absolutely crucial in real-world applications. In our proposed setting, the key objective is to construct a CBC together with a safety controller while providing a lower bound on the satisfaction probability of the safety property over a finite time horizon. We propose a systematic approach in the form of sum-of-squares optimization and matrix inequalities for the synthesis of CBC and its associated safety controller. We demonstrate the efficacy of our approach on a permanent magnet synchronous motor under a wireless communication network.