Computer Engineering and Applications ›› 2015, Vol. 51 ›› Issue (20): 240-245.

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Robust neural network control for a class of noncommensurate nonlinear fractional-order system

LI Anping1,2, LIU Guorong1,2, YANG Xiaoliang1, SHEN Xiqun2   

  1. 1.Institute of Electrical and Information Engineering, Hunan University, Changsha 410082, China
    2.College of Electrical and Information Engineering, Hunan Institute of Engineering, Xiangtan, Hunan 411104, China
  • Online:2015-10-15 Published:2015-10-30

一类非等阶分数阶非线性系统的神经网络控制

李安平1,2,刘国荣1,2,杨小亮1,沈细群2   

  1. 1.湖南大学 电气与信息工程学院,长沙 410082
    2.湖南工程学院 电气与信息工程学院,湖南 湘潭 411104

Abstract: The paper is concerned with the problem of the robust control for a class of fractional order noncommensurate nonlinear systems with positive real uncertainty and nonlinear functions unknown. Firstly, the unknown functions have been approximated using RBF neural networks, and by introducing a continuous frequency distributed model the fractional order system is an equivalent integral-order system with infinite dimension, then using indirect Lyapunov approach and Linear Matrix Inequality (LMI) techniques, the sufficient condition for robust asymptotic stability of the closed loop system is presented. The validity of the proposed methods is demonstrated by numerical example.

Key words: noncommensurate fractional order system, positive real uncertainty, Radical Basis Function(RBF) neural network, Linear Matrix Inequality(LMI)

摘要: 讨论一类不确定非线性分数阶非等阶(noncommensurate)的系统的控制问题。假设系统含的不确定包括正实不确定(positive real uncertainty)项和非线性函数完全未知,首先利用RBF神经网络近似未知非线性函数,再基于系统的连续频率分布模型将分数阶系统转化为等价的无穷维分布状态变量的整数阶系统,结合间接Lyapunov方法及线性矩阵不等式(LMI)方法,给出了系统鲁棒渐近稳定的充分条件。理论和实例仿真验证了方法的有效性。

关键词: 非等阶分数阶系统, 正实不确定, 径向基函数(RBF)神经网络, 线性矩阵不等式