Computation of time optimal controls by gradient matching

Time optimal control of nonlinear systems is considered. To find the optimal horizon, a sequence of fixed-horizon problems of minimizing an auxiliary cost functional is solved by gradient methods, with the use of adjoint trajectories. Basically, the control switching times are decision variables. The proposed computational methods of search for optimal horizon are based on an estimation-continuation strategy. The approach proved effective in the case of a cart-pendulum system.