Adaptive output regulation for two coupled anti-stable strings with unknown exosystem

¹ School of Mathematics and Physics, North China Electric Power University, Beijing 102206, PR China
² Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, PR China
³ School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, PR China
⁴ School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, PR China

^* Corresponding author: bzguo@iss.ac.cn

Received: 10 March 2024
Accepted: 23 February 2025

Abstract

This paper investigates non-collocated boundary output regulation for two interconnected anti-stable string systems, where external disturbances infiltrate the plant from both the spatial domain and the boundaries. The reference signal and disturbances originate from an unknown finite-dimensional exosystem. First, we design a state feedback controller using the backstepping transformation. Second, a Sylvester equation is employed to redirect disturbances from all channels to the output end. The exosystem is then transformed into an observable canonical form. Subsequently, an adaptive observer is developed, facilitating the design of a tracking error feedback controller that incorporates an adaptive internal model. We prove that the internal signals within the closed-loop system remain bounded, and the output signal successfully tracks the reference signal. Finally, the efficacy of our proposed scheme is verified through numerical simulations.