A simultaneous iterative solution technique for time-optimal control using dynamic-programming

A simultaneous iterative solution technique based on dynamic programming is presented as a reliable procedure for time-optimal control. By a simple transformation of the independent variable, t, the problem is converted to one of combined optimal parameter selection and optimal control. This approach allows us to find the optimal control policy that drives the system to the desired final state while searching for the optimal final time, tf simultaneously. Admissible values of the final time are randomly generated within a search region, and a direct search for the optimal final time, tfo is done iteratively only at the final time stage, with systematic region contraction, until convergence is attained. Significant savings in computation time can be realized using this approach instead of the traditional sequential approach.