This article presents a new study on adaptive control of multi-input and multi-output (MIMO) discrete-time nonlinear systems with a noncanonical form involving parametric uncertainties. The adaptive control scheme employs a vector relative degree formulation to reconstruct the noncanonical system dynamics and derives a normal form. Then, a new matrix decomposition-based adaptive control scheme is proposed for the controlled plant with a vector relative degree [1, 1, …, 1] under some relaxed design conditions. In particular, the matrix decomposition technique is adopted to overcome the singularity problem during the adaptive estimation of an uncertain high-frequency gain matrix. The adaptive control scheme ensures closed-loop stability and asymptotic output tracking. An extension to the adaptive control of general canonical-form MIMO discrete-time nonlinear systems is also presented. Finally, through simulations, the effectiveness of the proposed control scheme is verified. 

　　Publication: 

　　IEEE Transactions on Automatic Control. Volume: 67, Issue: 8, pp: 4330-4337. 

　　Author: 

　　Yanjun Zhang 

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

　　Email: yanjun@bit.edu.cn 

　　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 

　　Xiao-Kang Liu 

　　School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China 

　　Email: xiaokangliu@hust.edu.cn