Differential dynamic programming technique for optimal control

Continuous‐ and discrete‐time differential dynamic programming (DDP) approaches to solve general optimal control problems are described and analysed. A comparison of the two approaches shows the continuous‐time approach to be more general and flexible compared with the discrete‐time approach, since it is not tied to any discretization scheme. A comparison of DDP with the non‐linear programming (NLP) approach is also given. Three structural control problems — a linear model of a space structure, a single degree of freedom non‐linear impact absorber and a non‐linear flexible beam subjected to an impulsive load — are used to numerically evaluate the continuous‐ and discrete‐time DDP approaches. Several grid sizes are used to show that the continuous‐time approach with a reasonable number of grid points is more accurate and efficient (in most cases) than the discrete‐time approach. It is therefore recommended to fully develop and evaluate the technique for the optimal control of large‐scale systems.