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Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors

机译：基于近似误差界的估计的非线性系统鲁棒自适应模糊控制器

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摘要

This paper describes the design of the robust adaptive fuzzy controller for uncertain single-input single-output nonlinear dynamical systems with unknown nonlinearities. These unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy IF-THEN rules whose parameters are adjusted on-line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory. The Lyapunov synthesis approach is used to develop a state-feedback adaptive control algorithm based on the adaptive fuzzy model. The key assumption is that the reconstruction errors satisfy certain bounding conditions. The control law consists of two terms. One is the certainty equivalent control and the other is the bounding control. A bounding parameter adaptive law is used to obtain this bounding control. The overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded. It is also shown that, in the special case, the tracking error exponentially converges to zero even though the approximation errors exist.
机译：本文描述了具有未知非线性的不确定单输入单输出非线性动力学系统的鲁棒自适应模糊控制器的设计。这些未知的非线性是由模糊系统用一组模糊的IF-THEN规则来近似的，这些规则的参数根据一些自适应定律进行在线调整，目的是控制非线性系统的输出以跟踪给定的轨迹。李雅普诺夫综合方法用于开发基于自适应模糊模型的状态反馈自适应控制算法。关键假设是重建误差满足某些边界条件。控制律包括两个术语。一个是确定性等价控制，另一个是边界控制。边界参数自适应定律用于获得此边界控制。总体控制系统可确保跟踪误差收敛于零的小范围内，并且确保所涉及的所有信号均受均匀限制。还表明，在特殊情况下，即使存在近似误差，跟踪误差也会指数收敛至零。

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