Dealing with the uncertain high-frequency gain matrix, denoted as Kp, is a fundamental problem in multivariable adaptive control systems. In this article, we propose a new solution for parameter estimation and adaptive control for a general class of multi-input–multi-output discrete-time linear time-invariant systems. The proposed scheme does not require any prior knowledge of the sign or bound information of Kp, and thus, significantly relaxes the design conditions in traditional multivariable adaptive control systems. Compared with the commonly used Nussbaum gain or multimodel techniques for addressing the unknown signs of Kp, the proposed scheme does not rely on any additional design conditions or any switching mechanism, while still ensuring closed-loop stability and asymptotic output tracking. Specifically, an output feedback adaptive control law is developed based on a matrix decomposition technique, which leads to derivation of a modified estimation error model. Subsequently, a gradient-based parameter update law is formulated only relying on the nonzero condition of the leading principle minors of Kp. Through designing gain functions and stable filters, the controller is always nonsingular and does not involve any causal contradiction problem. Simulation study showcases the design process and demonstrates the effectiveness of the proposed scheme.

Publication:

IEEE Transactions on Automatic Control Volume: 70 June 2025

http://dx.doi.org/10.1109/TAC.2024.3513039

Author:

Yuchun Xu

the Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematics Sciences, University of Chinese Academy of Sciences, Beijing 100149, China

e-mail: xuyuchun@amss. ac.cn

Yanjun Zhang

the School of Automation, Beijing Institute of Technology, Beijing 100081, China, and also with State Key Lab of Automation Intelligent Unmanned Systems, Beijing Institute of Technology, Beijing 100081, China

e-mail: yanjun@bit.edu.cn

Ji-Feng Zhang

the School of Automation and Electrical Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China, also with the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and also with the School of Mathematics Sciences, University of Chines