Convexity verification for a hybrid chance constrained method in stochastic control problems

This paper is concerned with the verification of convexity for a class of stochastic control problems. In our previous work we proposed a hybrid method for solving the stochastic control problem with uncertainty in both the system and the constraint parameters. Under certain conditions, the optimization program is convex resulting in a drastic reduction in computational complexity over other methods. However, the previously proposed conditions for convexity are posterior checks on the results from the optimization program. In this work, we propose a finite cone cover method to a priori verify convexity. The method is established from a geometric approach which transforms the chance constraints into deterministic conditions. In addition, we also provide an efficient iterative partitioning algorithm to check the conditions. We demonstrate the effectiveness of the method on a stochastic motion planning example.