含参数不确定性的非线性分数阶系统输出反馈控制(英文)

Output feedback control for nonlinear fractional-order systems with parametric uncertainties

中文关键词  输出反馈控制  PI观测器设计  非线性分数阶系统  参数不确定性  渐近稳定性

英文关键词  output feedback control  PI observer design  nonlinear fraction-order systems  parametric uncertainties  asymptotic stability

中文摘要

      研究了具有参数不确定性的非线性分数阶系统的输出反馈控制问题. 为此, 首先提出一种新颖的分数阶比例积 分(PI)观测器对未知状态进行估计, 利用拉普拉斯变换和Gronwall-Bellman不等式得到观测器误差系统渐近稳定的充分 条件; 随后, 基于分数阶Lyapunov稳定性定理研究系统的输出反馈控制问题, 并分析相应闭环系统的渐近稳定性; 最后 给出了具体的数值仿真算例, 从而说明本文所得理论结果的有效性和适用性.

英文摘要

      This paper is concerned with the output feedback control problems of nonlinear fractional-order systems involving parametric uncertainties. Toward this aim, we first propose a novel fractional-order proportional integral (PI) observer to estimate the unknown state of the considered system. Sufficient conditions for asymptotical stability of the resulting observer error systems are then obtained by using the Laplace transformation and the Gronwall-Bellman inequality. Subsequently, output feedback control problem of the studied system is considered and asymptotic stability of corresponding closed-loop system is derived based on the fractional Lyapunov stability theorem. At last, to illustrate the effectiveness and practical applicability of our obtained theoretical results, we provide a detailed numerical example.