Optimal Mode-switching for Hybrid Systems with Unknown Initial State

This paper concerns an optimal control problem defined on a class of switchedmode hybrid dynamical systems. Such systems change modes whenever the state intersects certain surfaces that are defined in the state space. These switching surfaces are parameterized by a finite dimensional vector called the switching parameter. The optimization problem we consider is to minimize a given cost-functional with respect to the switching parameter under the assumption that the initial state of the system is not completely known. Instead, we assume that the initial state can be anywhere in a given set. We will approach this problem by minimizing the worst possible cost over the given set of initial states using results from minimax optimization. The results are then applied in order to solve a navigation problem in mobile robotics.