Offline periodic optimal event-triggered critic learning control for discrete-time nonlinear systems

This paper develops a novel offline periodic event-triggered control method via critic learning techniques for discrete nonlinear plants, which simultaneously addresses the requirements of computational efficiency and optimality. To overcome the implementation limitations of conventional event-based control approaches, the systemic structural framework is reconstructed to collect data information only at sampling instants. Subsequently, based on the stability of the controlled system, a constant triggering threshold is skillfully derived to determine the periodic interval, enabling predictable periodic updates of the control law while significantly reducing the computational burden. In the offline iterative training phase with the sampled data, the Hamilton–Jacobi–Bellman equation of the controlled system is addressed by building the model, critic, and action networks, ensuring convergence to optimal control policy. Finally, numerical simulations on two nonlinear systems validate the effectiveness of the proposed approach in terms of control accuracy, sampling reduction, and computational efficiency.