EVALUATION OF THE PARAMETERS USED IN ITERATIVE DYNAMIC-PROGRAMMING

To apply iterative dynamic programming (IDP) to optimal control problems having a very large number of control variables the use of randomly chosen values for control at each grid point is required. To gain insight into the effect of the number of allowable values for control, the region contraction factor, and the number of grid points for the state vector to be used, computational results are presented for two nonlinear systems, one of which possesses numerous local optima. The reliability of obtaining the global optimum for the bifunctional catalyst blend optimization problem was found to be somewhat higher by using randomly chosen values for control rather than by choosing the control values over a uniform distribution. The global optimum is obtained even when a small number of allowable values for control at each grid point and a small number of grid points for the states are used. There is a wide range of the region contraction factor for which rapid convergence to the optimum is obtained. Also the number of grid points for the state can be very small without adversely affecting convergence to the optimum.