This paper develops a singularity-free adaptive tracking control scheme for a general class of multi-input and multi-output uncertain discrete-time nonlinear systems with non-canonical control gain matrices. The estimation of the control gain matrices, especially in some non-canonical forms, may be singular during parameter adaptation, which leads to the singularity problems of the adaptive control laws. This paper employs the matrix decomposition technique to solve the problem under a linearly parameterized adaptive control framework. The state and output feedback cases are addressed, respectively, to ensure closed-loop stability and asymptotic output tracking. Compared with the existing results, the features of the proposed adaptive control scheme include: (i) the proposed control laws do not involve the high-gain issue commonly encountered in robust control methods; (ii) two different filtered tracking error signals are introduced for the state and output feedback cases, respectively. These filters are crucial to avoid causality contradiction of the adaptive control laws commonly encountered in adaptive control of discrete-time systems; and (iii) a future time signal estimation-based adaptive control law is developed to ensure asymptotic output tracking for the output feedback case without requiring the high-gain observer. Finally, an illustrative example is given to verify the validity of the proposed control scheme. 

　　Publication: 

　　Automatica, Volume 153, July 2023, 111054 

　　Author: 

　　Yuchun Xu 

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　School of Mathematics Sciences, University of Chinese Academy of Sciences, Bejing 100149, China 

　　Yanjun Zhang 

　　School of Automation, Beijing Institute of Technology, Beijing 100081, China 

　　Ji-Feng Zhang 

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 

　　School of Mathematics Sciences, University of Chinese Academy of Sciences, Bejing 100149, China 

　　Email: jif@iss.ac.cn