Computing Probabilistic Controlled Invariant Sets

This article investigates stochastic invariance for control systems through probabilistic controlled invariant sets (PCISs). As a natural complement to robust (RCISs), we propose finite-, and infinite-horizon PCISs, explore their relation RICSs. We design iterative algorithms compute the PCIS within given set. For with discrete spaces, computations of PCISs at each iteration are based on linear programming, mixed integer respectively. The computationally tractable, terminate in finite number steps. continuous show how discretize prove convergence approximation when computing finite-horizon PCISs. In addition, it is shown that an can be computed by backward reachable set from RCIS contained it. These applicable practical systems. Simulations illustrate effectiveness theoretical results motion planning.