Adaptive Neural Tracking Control of a Class of Hyperbolic PDE With Uncertain Actuator Dynamics
研究了一类边界执行器动力学由非线性常微分方程描述的双曲偏微分方程的自适应神经跟踪控制问题，首次提出跟踪控制方案，利用神经网络估计非线性，结合反步法设计控制器，并通过仿真验证。
This article investigates the adaptive neural tracking control problem for a class of hyperbolic PDE with boundary actuator dynamics described by a set of nonlinear ordinary differential equations (ODEs). Particularly, the control input appears in the ODE subsystem with unknown nonlinearities requiring to be estimated and compensated, which makes the control task rather difficult. It is the first time to consider tracking control of such a class of systems, rendering our contributions essentially different from the existing literature that merely focus on the stabilization problem. By formulating a virtual exosystem to generate a reference trajectory, we propose a novel design of the adaptive geometric controller for the considered system where neural networks (NNs) are employed to approximately estimate nonlinearities, and finite and infinite-dimensional backstepping techniques are leveraged. Moreover, rigorously theoretical proofs based on the Lyapunov theory are provided to analyze the stability of the closed-loop system. Finally, we illustrate the results through two numerical simulations.