Optimal Control for State-Dependent Switched Time-Delayed Systems

In this article, we investigate the optimal control problem of hybrid time-delayed systems. The time-delayed system has switched state-dependent dynamics and/or a switched performance index (PI). Conditions are given for controlling such hybrid time-delayed systems optimally. In particular, it is shown that the Euler-Lagrange equation is impulsive, and its integration provides relevant information for solving the problem directly without the necessity of parameter optimization. Simulation results confirm the interpretation of this generalized Euler-Lagrange equation.