Observer‐Based Optimal Neuro‐Control for Unknown Nonlinear Systems Subject to Input Constraints via a Dynamic Event‐Triggered Strategy

ABSTRACT This paper proposes a dynamic event‐triggered optimal control strategy for unknown nonlinear continuous‐time (CT) systems with input constraints based on a state observer and an identifier‐critic neural network (ICNN). Firstly, a discounted cost function is introduced to deal with the input constraints for the systems and establish a relevant Hamilton‐Jacobi‐Bellman (HJB) equation to solve the optimal control problem. Secondly, an observer is designed to reconstruct the state of the systems that relate to the information at the moment of event triggering. Then, to reduce communication and computation burdens, a dynamic event‐triggered control (DETC) strategy is applied to keep the signal transmissions and controller aperiodic update, which is better than the traditional static event‐triggered control (ETC) strategy and effectively excludes Zeno behavior. Moreover, to relax the assumptions about the dynamics of the systems and obtain the optimal solution of the HJB equation, an ICNN architecture is developed. The identifier neural network (INN) approximates the dynamics knowledge of unknown systems, and the given update law of the weight matrix ensures the convergence of the state errors. By the gradient descent method, the critic neural network (CNN) is used to approximate the optimal performance index function to approximate the solution of the modified HJB equation, and then the theoretical analysis proves the uniform ultimate boundedness (UUB) of the system states and the weight matrix of ICNN. Finally, the effectiveness of the proposed method is verified by a numerical simulation.