Boundary Tracking Control for An Unstable Wave Equation with Boundary Uncertainties: A Backstepping Adaptive NN Approach

• Published in: IEEE/ASME International Conference on Advanced Intelligent Mechatronics pp. 305 - 310
• Main Authors: Zhang, Jingting, Gu, Yan, Zeng, Wei, Yuan, Chengzhi
• Format: Conference Proceeding
• Language: English
• Published: IEEE 28.06.2023
• Subjects: Adaptation models; adaptive neural network; Adaptive systems; Artificial neural networks; Backstepping; boundary tracking control; Distributed parameter systems; Observers; Propagation; Uncertainty; wave equation
• DOI: 10.1109/AIM46323.2023.10196171

This paper investigates the tracking control problem of an unstable wave equation with boundary uncertainties. The wave equation under consideration has a negative damper (unstable) at the uncontrolled boundary and uncertain nonlinear dynamics at the controlled boundary. A novel boundary tracking control scheme is proposed by incorporating the backstepping method with adaptive neural networks (NN). Specifically, an adaptive radial basis function (RBF) NN model is first developed to approximate/counteract the system uncertainties. A boundary-feedback observer is then designed with such a NN model to estimate the overall state of the wave equation. Based on this, a boundary tracking controller is finally proposed using the adaptive backstepping technique. Uniquely, this new control scheme is capable of rendering stable state tracking (i.e., driving the system's holistic state to track a prescribed reference trajectory), significantly advancing the current literature that is largely focused on output tracking control. Rigorous analysis is performed to verify the well-posedness and stability of the overall closed-loop system. Simulation studies have been conducted to demonstrate effectiveness of the proposed results.