摘要
本文研究具状态约束 K与目标集 C之下的微分包含 x′( t)∈ F( x( t) )的极小时间函数 .主要证明了 :( 1 )存在有限时间 ,使在约束 K之下 ,微分包含的一条轨道可以到达 C;( 2 )极小时间函数是下半连续的且是相依 Hamilton- Jacobi方程的粘性上解 .
In this paper, the minimum time function for differential inclusion x′(t)∈F(x(t)) with state constraints K and target set C is studied. The main results are: (1) There exists a finite time, for which a trajectory of the differential inclusion reaches C under state constraints K; (2) The minimum time function is lower semicontinuous and it is a viscosity supersolution to the contingent Hamilton-Jacobi equation.
出处
《应用数学》
CSCD
2000年第2期31-36,共6页
Mathematica Applicata
基金
Projectssupported by the Science Commission of Gui Zhou University and Gui Zhou Province( N0 3 0 71)
关键词
微分包含
极小时间函数
生存理论
Differential inclusion
Minimum time function
Viability theory
