A Stochastic Approach to Maximal Output Admissible Sets and Reference Governors

This paper presents a stochastic approach to Reference Governors (RG) and Maximal Output Admissible Sets (MAS) using chance constraints. In order to construct a stochastic robustly invariant MAS (SR-MAS), we extend the earlier ideas in the literature to Lyapunov stable systems with output constraints. Formal proofs for important properties such as positive invariance and finite determinism of SR-MAS are provided. It is shown that the SR-MAS is less conservative than the deterministic approach. An algorithm is provided to compute the SR-MAS in finite time. Finally, we present a stochastic RG formulation, which leverages the SR-MAS. The main results are illustrated with a numerical simulation of a mass-spring-damper model with constraints imposed over the control signal and output.