摘要
本文讨论了一类广义非自治离散松驰系统的时间最优控制问题,将Rn中点曲线的目标约束推广为凸集值函数的超曲线约束.在证明了松驰系统与原系统可达集相等的基础上,得到了最优控制的存在性.由凸集分离定理及终端时间阈值函数方程,我们获得了最大值原理及最优控制时间的确定方法.较之Hamilton方法,本文的条件更一般.离散松驰系统的相关结论可以用于分散控制.
The paper discusses a generalized non-autonomous discrete relaxed system in time optimal control with generalizing the target constraint from the point curve to convex set hyper curve. Based on the equivalence of the reachable sets from an original system to its relaxed system, the existence of time optimal control is proved. Using separation theorem of convex set and the time terminal value function equation, we obtain the determining method of optimal terminal time as well as the Maximum principle. Compared with the Hamilton method, conditions involved in the paper are more general. And concerning results of the discrete relaxed control system in finite dimension can be used in the decentralized control.
出处
《应用数学》
CSCD
北大核心
2007年第1期24-30,共7页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(10101019)
关键词
时间最优控制
非自治松驰系统
终端集值约束
最大值原理
阀函数
Time optimal control
Non-autonomous relaxed system Terminal setvalue constraint Maximum principle Value function
