Numerical Solution of Minimax Problems of Optimal Control. Part 7. Multiple-Subarc Approach

摘要

This is the seventh report in a series dealing with the numerical solution of minimax problems of optimal control. This report considers the type of problem in which the minimax function depends on both the state and the control. Specific transformation techniques are presented for converting examples of this type problem into the Mayer-Bolza problem of the calculus of variations. Numerical solutions to the latter problem are then supplied by means of the multiple-subarc approach employed in conjunction with sequential gradient-restoration algorithms (SGRA). This is done to refine the solutions obtained using the single-subarc approach. It is found that the combination of transformation techniques and SGRA yield numerical solutions which are quite close to the known analytical solutions. The relative differences between the numerical values and the analytical values of the minimax performance index are of order 0.001 if the single-subarc approach is used and of order 0.0001 if the multiple-subarc approach is used.