# Some Eecient Algorithms for Unconstrained Discrete-time Optimal Control Problems

- 1993

#### Abstract

The diierential dynamic programming algorithm (DDP) and the stage-wise Newton procedure are two typical examples of eecient local procedures for discrete-time optimal 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 modiied \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 presented to compare these algorithms and the Coleman-Liao algorithm.