一类变结构动态系统的非光滑最优性条件

运筹学学报 ›› 2013, Vol. 17 ›› Issue (3): 65-72.

一类变结构动态系统的非光滑最优性条件

李丽花^1,2,*, 高岩¹, 王隔霞²

1. 上海理工大学管理学院, 上海 200093 2. 上海电力学院数理学院, 上海 200433

出版日期:2013-09-15 发布日期:2013-09-15
通讯作者: 李丽花 E-mail:dlxyllh2004@163.com
基金资助:
国家自然科学基金项目 (Nos. 11171221, 6120300), 上海市科委项目 (No. 10550500800), 上海市一流学科项目 (No. XTKX2012), 上海市自然科学基金青年项目 (No.12ZR1444400), 上海市研究生创新培育项目 (No. 5413303101)

Non-smooth optimality conditions for a class of dynamic systems with variable structure

LI Lihua^1,2,*, GAO Yan¹, WANG Gexia²

1. School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China 2. School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China

Online:2013-09-15 Published:2013-09-15

摘要/Abstract

摘要： 研究了一类事件驱动的变结构动态系统的非光滑最优性条件. 通过引入一个新的时间变量, 将变结构动态系统的最优性问题转化为古典动态系统的最优性问题. 基于广义微分和古典动态系统的最优性理论, 得到了该系统的Frechet上微分形式的必要性条件, 推广了已有文献的相关结论. 结果表明, 在系统的连续运行过程中, 控制变量、协态变量和状态变量满足最小值原理和协态方程. 在系统的运行模型发生改变时, 协态变量产生一定的跳跃, 哈密尔顿函数连续. 最后通过一个算例说明了该结论的有效性.

关键词: 最优性条件, 变结构动态系统, 非光滑分析

Abstract: In this paper, non-smooth optimality conditions for a class of event-driven dynamic systems with variable structure are investigated. By introducing a new time variable, the dynamical optimal problems with variable structure are transformed into classical optimal problems. Based on the knowledge of generalized differential and classical optimal theory, necessary optimality conditions of Frechet superdifferential form for this dynamic system are obtained, which generalize some existing relevant results. It is shown that, in the continuous process of the system, the control variable, the adjoint variable and the state variable satisfy the adjoint equations and the minimum principles. At the changing instants of the system model, the adjoint variables make certain jump and the Hamiltonian is continuous. At last, one example is given to illustrate the efficiency of the main results.

Key words: optimality condition, variable structural dynamical systems, nonsmooth analysis

中图分类号:

O231.2

李丽花, 高岩, 王隔霞. 一类变结构动态系统的非光滑最优性条件[J]. 运筹学学报, 2013, 17(3): 65-72.

LI Lihua, GAO Yan, WANG Gexia. Non-smooth optimality conditions for a class of dynamic systems with variable structure[J]. Operations Research Transactions, 2013, 17(3): 65-72.

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