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.
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Ng, C.K., Liao, LZ. & Li, D. A Globally Convergent and Efficient Method for Unconstrained Discrete-Time Optimal Control. Journal of Global Optimization 23, 401–421 (2002). https://doi.org/10.1023/A:1016595100139
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DOI: https://doi.org/10.1023/A:1016595100139