Time-optimal control of high-dimensional systems by iterative dynamic-programming

For time optimal control, the problem is first transformed into a finite dimensional optimization problem by using time stages of varying lengths to enable accurate switching, and then solved by iterative dynamic programming. In high dimensional systems it is necessary to ensure convergence to the global optimum. Incorporating penalty functions into the performance index and using an adequate number of stages can yield the global optimum. The use of a continuation approach, where the number of stages in an intermediate solution is systematically increased, appears to be more effective. Three linear systems are used to develop and to test the approaches.