A Globally Convergent and Efficient Method for Unconstrained Discrete-Time Optimal Control

Abstract

Shift schemes are commonly used in non-convex situations when solving unconstrained discrete-time optimal control problems by the differential dynamic programming (DDP) method. However, the existing shift schemes are inefficient when the shift becomes too large. In this paper, a new method of combining the DDP method with a shift scheme and the steepest descent method is proposed to cope with non-convex situations. Under certain assumptions, the proposed method is globally convergent and has q-quadratic local conve rgence. Extensive numerical experiments on many test problems in the literature are reported. These numerical results illustrate the robustness and efficiency of the proposed method.