Matrix Decomposition-Based Adaptive Control of Noncanonical Form MIMO DT Nonlinear Systems

Yanjun Zhang, Ji Feng Zhang, Xiao Kang Liu

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

—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.

Original languageEnglish
Pages (from-to)4330-4337
Number of pages8
JournalIEEE Transactions on Automatic Control
Volume67
Issue number8
DOIs
Publication statusPublished - 1 Aug 2022
Externally publishedYes

Keywords

  • Adaptive control
  • matrix decomposition
  • noncanonical form
  • output tracking

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