As is well known, traditional PID controllers are the most widely used type of controllers in industrial control due to their simplicity and other advantages. However, the existing research results on PID controllers lack a general theory for addressing the nonlinearity and uncertainty present in practical systems. In the era of intelligent control, it is highly valuable to design an intelligent PID controller with learning capability for complex unknown nonlinear systems. In this paper, we consider an extended form of PID controller based on deterministic learning (DL) for high-order nonlinear systems with unknown dynamics. The introduction of neural networks (NNs) provides an effective tool to compensate for the composite unknown nonlinearities in controlled systems, overcoming the limitations of traditional PID controllers relying solely on feedback mechanisms to combat unknown nonlinearities. Based on the Lyapunov theory, it not only ensures the stability and tracking control of the system but also simplifies the selection of controller parameters. Furthermore, based on the DL theory, the composite unknown nonlinear dynamics can be accurately compensated and approximated, and the acquired knowledge can be stored in a constant-value neural network. When encountering similar control tasks, the acquired knowledge can be quickly accessed to construct a knowledge-based extended PID controller, thereby improving the overall control performance. Simulation results demonstrate the effectiveness of the proposed algorithm.
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