Regular Papers

International Journal of Control, Automation and Systems 2016; 14(4): 893-905

Published online June 1, 2016

https://doi.org/10.1007/s12555-015-0054-7

© The International Journal of Control, Automation, and Systems

Concise Adaptive Fuzzy Control of Nonlinearly Parameterized and Periodically Time-varying Systems via Small Gain Theory

Guoqing Zhang and Xianku Zhang*

Dalian Maritime University

Abstract

This study is concerned with robust adaptive fuzzy stabilization of the nonlinearly parameterized and periodically time-varying system with known period of the parameterized disturbance. In this note, a novel uncertainty delivering approach is developed to overcome the problems: “the initial evident oscillating error”, “explosion of complexity” and “curse of dimensionality” from the root causes that are common in the current literatures on approximation-based algorithms. Furthermore, a novel adaptive fuzzy control scheme is proposed with advantages of concise structure and easy-to-implementation in practical engineering. Only one fuzzy type approximator is introduced to compensate uncertainties of the whole system in the scheme. Based on small gain theory, all signals of the composite closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, three simulation experiments are presented to demonstrate the effectiveness of our results.

Keywords Adaptive control, fuzzy set, nonlinear parameterized systems, periodically time-varying disturbances, small gain theory.

Article

Regular Papers

International Journal of Control, Automation and Systems 2016; 14(4): 893-905

Published online August 1, 2016 https://doi.org/10.1007/s12555-015-0054-7

Copyright © The International Journal of Control, Automation, and Systems.

Concise Adaptive Fuzzy Control of Nonlinearly Parameterized and Periodically Time-varying Systems via Small Gain Theory

Guoqing Zhang and Xianku Zhang*

Dalian Maritime University

Abstract

This study is concerned with robust adaptive fuzzy stabilization of the nonlinearly parameterized and periodically time-varying system with known period of the parameterized disturbance. In this note, a novel uncertainty delivering approach is developed to overcome the problems: “the initial evident oscillating error”, “explosion of complexity” and “curse of dimensionality” from the root causes that are common in the current literatures on approximation-based algorithms. Furthermore, a novel adaptive fuzzy control scheme is proposed with advantages of concise structure and easy-to-implementation in practical engineering. Only one fuzzy type approximator is introduced to compensate uncertainties of the whole system in the scheme. Based on small gain theory, all signals of the composite closed-loop system are guaranteed to be uniformly ultimately bounded. Finally, three simulation experiments are presented to demonstrate the effectiveness of our results.

Keywords: Adaptive control, fuzzy set, nonlinear parameterized systems, periodically time-varying disturbances, small gain theory.

IJCAS
May 2024

Vol. 22, No. 5, pp. 1461~1759

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