计算机工程与应用
計算機工程與應用
계산궤공정여응용
Computer Engineering and Applications
2015年
20期
240-245
,共6页
李安平%刘国荣%杨小亮%沈细群
李安平%劉國榮%楊小亮%瀋細群
리안평%류국영%양소량%침세군
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
非等階分數階繫統%正實不確定%徑嚮基函數(RBF)神經網絡%線性矩陣不等式
비등계분수계계통%정실불학정%경향기함수(RBF)신경망락%선성구진불등식
noncommensurate fractional order system%positive real uncertainty%Radical Basis Function(RBF)neural network%Linear Matrix Inequality(LMI)
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。
討論一類不確定非線性分數階非等階（noncommensurate）的繫統的控製問題。假設繫統含的不確定包括正實不確定（positive real uncertainty）項和非線性函數完全未知，首先利用RBF神經網絡近似未知非線性函數，再基于繫統的連續頻率分佈模型將分數階繫統轉化為等價的無窮維分佈狀態變量的整數階繫統，結閤間接Lyapunov方法及線性矩陣不等式（LMI）方法，給齣瞭繫統魯棒漸近穩定的充分條件。理論和實例倣真驗證瞭方法的有效性。
토론일류불학정비선성분수계비등계（noncommensurate）적계통적공제문제。가설계통함적불학정포괄정실불학정（positive real uncertainty）항화비선성함수완전미지，수선이용RBF신경망락근사미지비선성함수，재기우계통적련속빈솔분포모형장분수계계통전화위등개적무궁유분포상태변량적정수계계통，결합간접Lyapunov방법급선성구진불등식（LMI）방법，급출료계통로봉점근은정적충분조건。이론화실례방진험증료방법적유효성。
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 sys-tem is presented. The validity of the proposed methods is demonstrated by numerical example.
