Computation of Approximately Optimal Control Signals for Systems With Time Delays

A computational algorithm is presented for a class of optimal control problems involving time delays. The approach is to restrict the control signal to a class of piecewise constant time functions with a prescribed number of switching times, compute the optimal member of this class, and then repeat with a larger number of switching times. By allowing the number of switching times to increase beyond bound a sequence of restricted optimal control signals is developed whose limit approaches the unrestricted optimal control signal. In practice the computations are terminated after a finite number of repeats, thus leading to the approximate nature of the solution. The results of two examples are included to illustrate the technique.