Dynamic Optimization of Path-Constrained Switched Systems with Multiple Time-Delays

A dynamic optimization algorithm is designed for the optimal control problem of path-constrained switched systems with multiple time-delays. Firstly, the control vector parametrization technique is utilized to parameterize continuous control input into finite numbers of piecewise constant functions. Then, the gradient information of the objective function with respect to the decision variables (switching times and control input) is evaluated by solving an auxiliary costate system. Secondly, the dynamic optimization algorithm based on the gradient information is proposed to locate an optimal solution of the path-constrained switched systems with multiple time-delays, which satisfies the Karush-Kuhn-Tucker conditions to a specific tolerance, meanwhile guaranteeing rigorous satisfaction of the path constraints. Thirdly, it is proved that the proposed algorithm terminates within finite iterations. Finally, the developed algorithm is validated through a numerical simulation.