DIFFERENTIAL DYNAMIC-PROGRAMMING TECHNIQUE FOR OPTIMAL-CONTROL

Continuous- and discrete-time differential dynamic programming (DDP) a pproaches 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-t ime approach, since it is not tied to any discretization scheme. A com parison of DDP with the non-linear programming (NLP) approach is also given. Three structural control problems - a linear model of a space s tructure, 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 efficien t (in most cases) than the discrete-time approach. It is therefore rec ommended to fully develop and evaluate the technique for the optimal c ontrol of large-scale systems.