Composite Learning Based Adaptive Control of Linear 2 × 2 Hyperbolic PDE Systems

• Published in: IEEE transactions on cybernetics Vol. 55; no. 1; pp. 295 - 306
• Main Authors: Xiao, Yu, Feng, Yun, Luo, Biao, Li, Hanxiong, Xu, Xiaodong
• Format: Journal Article
• Language: English
• Published: United States IEEE 2025
• Subjects: Accuracy; Adaptive control; Asymptotic stability; Backstepping; composite learning; Convergence; distributed parameter system; exponential convergence; Iron; Numerical stability; Parameter estimation; uncertain parameters; Uncertainty; Vectors
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2024.3485546

This article considers the adaptive stability control of a class of <inline-formula> <tex-math notation="LaTeX">2\times 2 </tex-math></inline-formula> linear hyperbolic PDE systems. The PDE model is subject to constant but in-domain and boundary unknown parameters. A novel adaptive controller is developed by leveraging the swapping design technique and composite parameter learning law. With swapping design, several linear and static combinations, including carefully designed filters, unknown parameters, and error terms, are constructed to express the system states. From the static combinations, a composite learning based forgetting-factor least squares law is introduced to guarantee exponential parameter convergence without the persistent excitation (PE). Although inaccurate parameter estimation in the adaptive backstepping control results in asymptotic stability of the system, accurate parameter estimation ensures the exponential convergence of closed-loop system and concomitantly improves the transient performance. Finally, a comparative numerical simulation is performed to validate the effectiveness and advantage of the developed adaptive control scheme.