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首页> 外文期刊>International journal of machine learning and cybernetics >Adaptive control of nonlinear fractional-order systems using T-S fuzzy method
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Adaptive control of nonlinear fractional-order systems using T-S fuzzy method

机译：基于T-S模糊方法的非线性分数阶系统的自适应控制

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摘要

Owing to the superior capability of fractional differential equations in modeling and characterizing accurate dynamical properties of many high technology real world systems, the design and control of fractional-order systems have captured lots of attention in recent decades. In this paper, an adaptive intelligent fuzzy approach to controlling and stabilization of nonlinear non-autonomous fractional-order systems is proposed. Since dynamic equations of applied fractional-order systems usually contain various parameters and nonlinear terms, the Takagi-Sugeno (T-S) fuzzy models with if-then rules are adopted to describe the system dynamics. Also, as the nonlinear system parameters are assumed to be unknown, adaptive laws are derived to estimate such fluctuations. Simple adaptive linear-like control rules are developed based on the T-S fuzzy control theory. The stability of the resulting closed loop system is guaranteed by Lyapunov's stability theory. Two illustrative numerical examples are presented to emphasize the correct performance and applicability of the proposed adaptive fuzzy control methodology. It is worth to notice that the proposed controller works well for stabilization of a wide class of either autonomous nonlinear uncertain fractional-order systems or non-autonomous complex systems with unknown parameters.
机译：由于分数阶微分方程在建模和表征许多高科技现实世界系统的精确动力学特性方面的卓越能力，分数阶系统的设计和控制在近几十年来引起了很多关注。本文提出了一种自适应智能模糊方法，用于控制非线性非自治分数阶系统。由于应用分数阶系统的动力学方程通常包含各种参数和非线性项，因此采用具有if-then规则的Takagi-Sugeno（T-S）模糊模型来描述系统动力学。另外，由于假定非线性系统参数未知，因此导出了自适应定律以估计这种波动。基于TS模糊控制理论，提出了简单的自适应线性控制规则。李雅普诺夫的稳定性理论保证了所得闭环系统的稳定性。给出两个说明性的数值示例，以强调所提出的自适应模糊控制方法的正确性能和适用性。值得一提的是，所提出的控制器对于稳定种类繁多的自主非线性不确定分数阶系统或具有未知参数的非自主复杂系统的稳定性很好。

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