Design of an event-triggered adaptive dynamic programming-based prescribed-time control system

To address the problems of resource waste in continuous-time nonlinear systems, as well as the defects of existing integrated adaptive dynamic programming and sliding mode control schemes (e.g. non-presettable convergence time and high resource consumption), this paper proposes a prescribed-time optimal robust input-constrained control strategy integrating sliding mode control and event-triggered adaptive dynamic programming with disturbance consideration. The proposed event-triggering condition is derived in consistency with the Lyapunov function decrease condition. Therefore, the triggering threshold ensures that the Lyapunov derivative remains negative definite between two consecutive events. Furthermore, the designed triggering condition ensures that the prescribed-time Lyapunov stability condition is consistently satisfied during the entire inter-event interval, and Zeno behavior is excluded. First, a fusion framework embedding prescribed-time constraints into event-triggered adaptive dynamic programming is constructed, where the prescribed-time function is incorporated into the control law derivation to achieve the synergy of prescribed-time convergence, resource saving, optimality, and robustness. Second, a reasonable threshold-based event-triggered condition is designed, and the non-zero length of the triggering interval is strictly proven to avoid the Zeno phenomenon. Finally, theoretical analysis and simulation results demonstrate that the system can converge within the preset time T with low resource consumption and excellent control performance, providing an effective solution for the prescribed-time control of nonlinear systems in resource-constrained scenarios.