Near-optimal control of nonlinear switched systems with non-cooperative switching rules

This paper presents a predictive, planning algorithm for nonlinear switched systems where there are two switching signals, one controlled and the other uncontrolled, both subject to constraints on the dwell time after a switch. The algorithm solves a minimax problem where the controlled signal is chosen to optimize a discounted sum of rewards, while taking into account the worst possible uncontrolled switches. It is an extension of a classical minimax search method, so we call it optimistic minimax search with dwell time constraints, OMSδ. For any combination of dwell times, OMSδ returns a sequence of switches that is provably near-optimal, and can be applied in receding horizon for closed loop control. For the case when the two dwell times are the same, we provide a convergence rate to the minimax optimum as a function of the computation invested, modulated by a measure of problem complexity. We show how the framework can be used to model switched systems with time delays on the control channel, and provide an illustrative simulation for such a system with nonlinear modes.