Optimistic planning for near-optimal control of nonlinear systems with hybrid inputs

Abstract

We propose an optimistic planning, branch-and-bound algorithm for nonlinear optimal control problems in which there is a continuous and a discrete action (input). The dynamics and rewards (negative costs) must be Lipschitz but can otherwise be general, as long as certain boundedness conditions are satisfied by the continuous action, reward, and Lipschitz constant of the dynamics. We investigate the structure of the space of hybrid-input sequences, and based on this structure we propose an optimistic selection rule for the subset with the largest upper bound on the value, and a way to select the largest-impact action for further refinement. Together, these fully define the algorithm, which we call OPHIS: optimistic planning for hybrid-input systems. A near-optimality bound is provided together with empirical results in two nonlinear problems where the algorithm is applied in receding horizon.