Parameter Sensitivity Analysis of Controlled Invariant Sets via Value Iteration

In this paper we propose a value-iteration based algorithm to compute controlled invariant sets in cases where the range of certain parameters in the system model are not known a priori. By defining the value function in a way that is related to parameter ranges, the proposed computation allows us to analyze parameter sensitivity for the controlled invariant set. The convergence properties of the algorithm are analyzed for certain classes of systems. Finally, a vehicle team power management case study is used to illustrate the efficacy and scalability of the proposed algorithm.