Adaptive neural optimal control for pure‐feedback nonlinear systems with prescribed performance and error compensating mechanism

Abstract This paper is concerned with the issue of adaptive neural optimal dynamic surface control (DSC) for uncertain pure‐feedback nonlinear systems with prescribed performance and unmodeled dynamics. A dynamic signal generated via an auxiliary linear system is employed to dispose of unmodeled dynamics. The adaptive prescribed performance tracking control is constructed by hyperbolic tangent function, which ensures that tracking error is in a specific area. The whole controller is composed of feedforward controller and feedback optimal controller. First, the feedforward controller is designed with the help of command filter and error compensating mechanism. In the meantime, the designed first‐order filter in the traditional DSC is displaced by using the second‐order stable linear systems. Second, by the aid of adaptive dynamic programming (ADP) method, neural networks (NNs) are utilized to estimate the optimal cost index and the optimal input. The updating laws of unknown neural network weights are constructed by gradient descent method and ‐modification approach. All the signals in the controlled system are proved to be semi‐globally uniformly ultimately bounded (SGUUB) via theoretical analysis. Finally, the simulation curves of numerical examples verify the feasibility of the constructed control strategy.