Matrix Decomposition-Based Adaptive Control of Noncanonical Form MIMO DT Nonlinear Systems (Ji-Feng Zhang)

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09 09, 2022

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

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