An Algorithm for Time-Optimal Control Problems

Abstract

A numerical procedure to compute nonsingular, time-optimal solutions for nonlinear systems, which have fixed initial and final states, and are linear and bounded in control, is presented. Using the Pontryagin’s Minimum Principle, the corresponding nonlinear two-point boundary-value problem is formulated and solved by combination of the forward-backward and the shooting methods. The forward-backward procedure generates a good guess of the initial costates, which is crucial for the convergence of the shooting method. Numerical example of a two-link manipulator illustrates the proposed approach and the convergence of the procedure.