Differential dynamic programming and optimal control of inequality constrained continuous dynamic systems

In this thesis, the development of the differential dynamic programming (DDP) algorithm is extensively reviewed from its introduction to its present status. Following this review, the DDP algorithm is shown to be readily adapted to handle inequality constrained continuous optimal control problems. In particular, a new approach using multiplier penalty functions implemented in conjunction with the DDP algorithm, is introduced and shown to be effective. Emphasis is placed on the practical aspects of implementing and applying DDP algorithm variants. The new DDP and multiplier penalty function algorithm variant is then tested and compared with established DDP algorithm variants as well as another numerical method before being applied to solve a problem involving the control of a robot arm in the plane.