发表机构
Universidade Federal de Minas Gerais; Instituto Federal de Educação, Ciência e Tecnologia de Minas Gerais（米纳斯吉拉斯联邦大学; 米纳斯吉拉斯联邦教育、科学和技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种局部递归最小二乘自适应模糊控制方法，通过规则独立协方差与激活式更新降低内存并保证误差有界，并给出LMI综合条件，在三个数值示例中验证了有效性。
AI 中文摘要
本文针对以准线性参数变化（qLPV）/Takagi-Sugeno（TS）形式表示的非线性系统的离散时间自适应模糊控制，提出了一种局部递归最小二乘（RLS）估计策略。未知非线性项由具有常值后件的TS模糊模型逼近，后件参数通过带遗忘因子的隶属函数加权RLS法则进行更新。所提出的估计器为每条规则保持不同的协方差，从而显著减少了最小二乘更新的内存占用。由于每条规则仅在其激活时进行自适应，自适应过程也得以简化。基于这些特性，我们能够证明该自适应法则确保局部自适应误差有界。在此基础上，针对匹配、扇区有界和范数有界的未知非线性，给出了线性矩阵不等式（LMI）综合条件，保证了闭环自适应控制系统的一致最终有界性。通过三个数值示例说明了三种情况下的自适应控制条件：具有未知重力方向的平面机械臂、具有未知耦合的两水箱系统，以及作为高效车辆推力的无刷直流（BLDC）电机。
英文摘要
This paper proposes a local recursive least squares (RLS) estimation strategy for discrete-time adaptive fuzzy control of nonlinear systems represented in quasi-Linear Parameter Varying (qLPV)/Takagi--Sugeno (TS) form. Unknown nonlinear terms are approximated by a constant-consequent TS fuzzy model, and the consequent parameters are updated by a membership-function-weighted RLS law with a forgetting factor. The proposed estimator keeps a different covariance for each rule, considerably reducing the memory footprint of the least-squares updates. The adaptation is also simplified since each rule is only adapted when it is active. From these properties, we are capable of showing that the adaptation law ensures bounded local adaptation errors. Building upon this adaptation law, Linear Matrix Inequality (LMI) synthesis conditions are presented for matched, sector-bounded and norm-bounded unknown nonlinearities, guaranteeing ultimate uniform boundedness of the adaptive control system in closed loop. Three numerical examples are presented to illustrate the adaptive control conditions in the three cases: a planar manipulator with unknown gravity direction, a two-tank system with unknown coupling, and a Brushless DC (BLDC) motor acting as thrust for an efficiency vehicle.
Comments47 pages, initial submission to the Journal of the Franklin Institute - no line numbers
