Some Efficient Algorithms for Unconstrained Discrete-time Optimal Control Problems

Abstract

The differential dynamic programming algorithm (DDP)and the stagewise Newton procedure are two typical examples of efficient local procedures for discrete-timeoptimal control (DTOC) problems. It is desirable to generalize these local procedures to globally convergent methods. One successful globalization was recently proposed by Coleman and Liao [3] which combines the trust region idea with Pantoja's stagewise Newton procedure. In this paper, we propose several algorithms for DTOC problems which combine a modified "dogleg" algorithm with DDP or Pantoja's Newton procedure. These algorithms possess advantages of both the dogleg algorithm and the DDP or the stagewise procedure, i.e.,they have strong global and local convergence properties yet remain economical. Numerical results are presentedto compare these algorithms and the Coleman-Liao algorithm.