Event-triggered optimal control with finite-time convergence critic networks for input-constrained nonlinear systems

This paper proposes an adaptive critic design-based event-triggered optimal control method for input-constrained continuous-time nonlinear systems. Adaptive critic design is a special framework of adaptive dynamic programming that approximates the value function by a critic neural network and derives the approximate optimal control policy through analytical methods. The proposed adaptive critic design considers the control input constraints by introducing a non-quadratic cost function and employs an event-triggered mechanism to reduce the number of controller executions. Unlike the existing event-triggered adaptive critic design, this paper proposes a novel finite-time adaptive law based on regression filtering scheme. The adaptive law utilizes the error information of the network weights to ensure fast convergence to the optimal control law under the event-triggered mechanism, which improves the real-time performance of the system. Additionally, explicit bounds for each parameter in the compact set and the specific convergence time estimates are provided in the convergence analysis. Finally, the effectiveness and practicality of the proposed method for real-time online applications are validated through two simulation examples.