Event-Triggered Optimal Control for Partially Unknown Constrained-Input Systems via Adaptive Dynamic Programming

Event-triggered control has been an effective tool in dealing with problems with finite communication and computation resources. In this paper, we design an event-triggered control for nonlinear constrained-input continuous-time systems based on the optimal policy. Constraints on controls are handled using a bounded function. To learn the optimal solution with partially unknown dynamics, an online adaptive dynamic programming algorithm is proposed. The identifier network, the critic network, and the actor network are employed to approximate the unknown drift dynamics, the optimal value, and the optimal policy, respectively. The identifier is tuned based on online data, which further trains the critic and actor at triggering instants. A concurrent learning technique repeatedly uses past data to train the critic. Stability of the closed-loop system, and convergence of neural networks to the optimal solutions are proved by Lyapunov analysis. In the end, the algorithm is applied to the overhead crane system to observe the performance. The event-triggered optimal controller with constraints stabilizes the system and consumes much less sampling times.