应用数学
應用數學
응용수학
MATHEMATICA APPLICATA
2007年
1期
24-30
,共7页
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
時間最優控製%非自治鬆馳繫統%終耑集值約束%最大值原理%閥函數
시간최우공제%비자치송치계통%종단집치약속%최대치원리%벌함수
Time optimal control%Non-autonomous relaxed system%Terminal set-value constraint%Maximum principle%Value function
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.
本文討論瞭一類廣義非自治離散鬆馳繫統的時間最優控製問題,將Rn中點麯線的目標約束推廣為凸集值函數的超麯線約束.在證明瞭鬆馳繫統與原繫統可達集相等的基礎上,得到瞭最優控製的存在性.由凸集分離定理及終耑時間閾值函數方程,我們穫得瞭最大值原理及最優控製時間的確定方法.較之Hamilton方法,本文的條件更一般.離散鬆馳繫統的相關結論可以用于分散控製.
본문토론료일류엄의비자치리산송치계통적시간최우공제문제,장Rn중점곡선적목표약속추엄위철집치함수적초곡선약속.재증명료송치계통여원계통가체집상등적기출상,득도료최우공제적존재성.유철집분리정리급종단시간역치함수방정,아문획득료최대치원리급최우공제시간적학정방법.교지Hamilton방법,본문적조건경일반.리산송치계통적상관결론가이용우분산공제.
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.
