MIMO fuzzy adaptive control systems based on fuzzy semi-tensor product

Hongli Lyu; Yanan Lyu; Yongchao Gao; Heng Qian; Shan Du; Hongli Lyu; Yanan Lyu; Yongchao Gao; Heng Qian; Shan Du

doi:10.3934/mmc.2023026

Mathematical Modelling and Control

2023, Volume 3, Issue 4: 316-330. doi: 10.3934/mmc.2023026

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MIMO fuzzy adaptive control systems based on fuzzy semi-tensor product

1.
Department of Electrical and Computer Engineering, Lakehead University, Thunder Bay, O. N., Canada
2.
Department of Fundamental Courses, Shandong University of Science and Technology, Tai'an, China
3.
Shandong Computer Science Center (National Supercomputer Center in Ji'nan), Qilu University of Technology (Shandong Academy of Science), Ji'nan, China
4.
Department of Computer Science, Mathematics, Physics and Statistics, Irving K. Barber Faculty of Science, University of British Columbia Okanagan, Kelowna, Canada

Received: 30 December 2022 Revised: 01 April 2023 Accepted: 25 April 2023 Published: 13 December 2023

Based on fuzzy semi-tensor product (STP) algorithms and fuzzy relation matrix (FRM) models, the design of an adaptive fuzzy controller was proposed in this paper for the multivariable nonlinear systems with uncertainty. The controlled multi-input-and-multi-output (MIMO) plants were expressed and processed first by FRM models and fuzzy STP operations, and then the indirect adaptive fuzzy control laws were designed. The tracking property of the FRM models was proved for the control objective of MIMO systems. The effectiveness of the novel matrix expression was verified by simulations of the tracking control on a two-link rigid robot manipulator. Results in simulation tests show that the proposed design of adaptive FRM control is efficient for nonlinear multivariables. Therefore, the proposed indirect fuzzy adaptive controllers can be extended to general matrix expression for MIMO nonlinear systems with fuzzy STP algorithms and FRM models and online approximate unknown parameters, according to required accuracy.
- adaptive control,
- FRM,
- MIMO nonlinear systems,
- STP
Citation: Hongli Lyu, Yanan Lyu, Yongchao Gao, Heng Qian, Shan Du. MIMO fuzzy adaptive control systems based on fuzzy semi-tensor product[J]. Mathematical Modelling and Control, 2023, 3(4): 316-330. doi: 10.3934/mmc.2023026

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Abstract

Based on fuzzy semi-tensor product (STP) algorithms and fuzzy relation matrix (FRM) models, the design of an adaptive fuzzy controller was proposed in this paper for the multivariable nonlinear systems with uncertainty. The controlled multi-input-and-multi-output (MIMO) plants were expressed and processed first by FRM models and fuzzy STP operations, and then the indirect adaptive fuzzy control laws were designed. The tracking property of the FRM models was proved for the control objective of MIMO systems. The effectiveness of the novel matrix expression was verified by simulations of the tracking control on a two-link rigid robot manipulator. Results in simulation tests show that the proposed design of adaptive FRM control is efficient for nonlinear multivariables. Therefore, the proposed indirect fuzzy adaptive controllers can be extended to general matrix expression for MIMO nonlinear systems with fuzzy STP algorithms and FRM models and online approximate unknown parameters, according to required accuracy.

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