广义Birkhoff系统分数阶最优控制问题的Noether定理  

Noether Theorem for Fractional Optimal Control Problems of Generalized Birkhoffian Systems

作　　者：贾秋丽[1] 魏风军[2] JIA Qiui;WEI Fengjun(School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang Henan 471023,China;School of Art and Design,Henan University of Science and Technology,Luoyang Henan 471023,China)

机构地区：[1]河南科技大学数学与统计学院,河南洛阳471023 [2]河南科技大学艺术与设计学院,河南洛阳471023

出　　处：《湖南工业大学学报》2024年第4期93-97,共5页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(11672032);河南科技大学博士科研启动基金资助项目(13480065)。

摘　　要：探讨了广义Birkhoff系统分数阶最优控制问题的Noether定理。首先,基于Caputo分数阶导数提出广义Birkhoff系统的分数阶最优控制问题,并运用分数阶变分方法得到了广义Birkhoff系统的分数阶最优控制问题的极值条件。然后,运用分数阶微积分和分数阶变分方法讨论了泛函在无穷小变换群作用下的不变性,分别给出了其时间不变和时间变化情况下的分数阶最优控制问题的Noether定理。最后,应用实例显示方法的有效性。An research has been made of the Noether theorem for fractional order optimal control problems of generalized Birkhoff systems.Firstly,based on Caputo fractional derivative,fractional optimal control problems have been proposed for generalized Birkhoff systems,thus obtaining the extremum conditions for fractional optimal control problems of generalized Birkhoff systems by using fractional calculus and fractional variations.Then,an investigation is made of the invariance of functionals under the action of infinitesimal transformation groups by adopting fractional calculus and variational methods,thus providing the Noether theorem for fractional optimal control problems under time invariant and time variation conditions,respectively.Finally,application examples are given to verify the effectiveness of the proposed method.

关 键 词：广义BIRKHOFF系统 NOETHER定理 最优控制 守恒量 

分 类 号：O316[理学—一般力学与力学基础]