A New Computational Method for a Class of Free Terminal Time Optimal Control Problems

Abstract

We develop a numerical method for solving an optimal control problem whose terminal time is not fixed, but is instead determined by a state-dependent stopping criterion. The main idea of this method is to approximate hte control by a piecewise constant function whose values and switching times are decision variables to be determined optimally. The optimal control problem then becomes an optimization problem with a finite number of decision variables. We develop a novel method for computing the gradient of the cost function in this approximate problem. On this basis, the approximate problem can be solved using any gradient-based optimization technique. We use this approach to solve an aeronautical control problem involving a gliding projectile. We also prove several important convergence results that justify our approximation scheme.