Computation of quantized controls using differential dynamic programming

A computational method developed by Jacobson is used for solving quantized control problems. At each iteration, the system equations are integrated forward in time using the current nominal control, and accessory equations, which yield the changes in the switch times of the optimal control, are integrated in reverse to obtain an improved control. This improved control is then used as the new nominal control for the next iteration. By continued iteration, the procedure produces control functions which successively improve the approximation to the optimal control function,