Optimal control for a class of input-constrained nonlinear switched systems

This paper investigates the optimal control problem for a class of nonlinear switched systems with input constraints. First, a non-quadratic finite-horizon performance index is constructed, in which the input constraint is explicitly embedded into the control cost. Accordingly, the derived optimal control law inherently satisfies the actuator constraints without requiring additional mechanisms to handle these constraints. Within the Hamiltonian framework, the optimal control law and optimal switching law are derived, and their intrinsic relationship is consequently revealed. To address the difficulty of analytically solving the optimal value function for the considered systems, a critic network is developed for online approximation of the optimal value function. In addition, an event-triggering mechanism is further introduced to update both control inputs and switching signals only at triggering instants, thereby reducing computation and communication resource consumption. Rigorous theoretical analysis verifies that Zeno behavior is excluded by the event-triggering mechanism, and that the minimum dwell-time constraint ensures well-posed switching by preventing excessively frequent mode transitions. Moreover, the proposed method guarantees closed-loop stability of the input-constrained nonlinear switched system. Finally, simulation results validate the effectiveness of the proposed approach.