Event-triggered optimal trajectory tracking control of underactuated ships based on goal representation heuristic dynamic programming

In this paper, a new event-triggered optimal trajectory tracking control method based on goal representation heuristic dynamic programming (GrHDP) is proposed for underactuated ships, which achieves the promising tracking performance, the minimized control energy consumption and the communication resource saving together. The adaptive event-triggered mechanism is designed from the performance perspective based on the internal reinforcement signals and the optimal value function. The trajectory tracking control algorithm is derived based on GrHDP value iteration by using three neural networks (NNs), and the underactuated problem can thereby be solved. Then, the approximation error between the GrHDP value iteration function and the optimal cost is theoretically analyzed, and the convergence of the GrHDP value iteration algorithm is proved. We discuss in detail the uniformly ultimately bounded (UUB) stability of the closed-loop system. A theoretical analysis is conducted on the parameter selection of the triggering condition, which compromises the communication resources and the control performance. The optimality of the proposed control scheme is finally verified through simulation.