状态和控制均含时滞的受外界扰动的线性系统的最优控制  

The Optimal Control of A Kind of System Affected By External Disturbance with Both State-and Control Input-Delay

作　　者：司家芳[1] 蒋威[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230039

出　　处：《数学的实践与认识》2010年第9期164-172,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10771001);教育部博士学科点专项科研基金(20093401110001);安徽省高校自然科学研究重大项目(KJ2010ZD02)

摘　　要：主要研究一类受外界持续扰动且状态和控制含不同时滞的线性系统的最优控制,首先通过变量代换,将系统化为控制不含时滞的滞后型微分系统.接着使用最优控制的极大值原理的必要条件,得到含超前和滞后项的两点边值问题.为了得到最优控制律的解析解,引进一个灵敏参数ε,得到两点边值问题序列,通过迭代法,得到最优控制律的解析解.并对外界扰动状态构造降维观测器,来实现最优控制律的物理可实现性.最后实例验证了上述方法的有效性.This article is designed to research the optimal control of a kind of system affected by external disturbance with both state- and control input-delay. At first, we can transform the initial system into a system with no control input-delay. Next use the necessary condition of maximum principle, we can obtain two-point boundary value problem with advance- and delay-terms.In order to get the analytic solution, we can introduce a sensitivity parameter, then a series of two-point boundary value problems are obtained. By the method of iteration, the optimal control is gained. By designing a reduced-dimension observer for external disturbance, the physical realization of optimal control can be realized. Finally, a example is showed to explain the validity of the above method.

关 键 词：外界扰动 状态时滞 控制时滞 最优控制 降维观测器 

分 类 号：O232[理学—运筹学与控制论]