扩散方程在可测集上的能观性估计和时间最优控制bang-bang性  

Observability from measurable sets for diffusion equations and the bang-bang property of time optimal controls

作　　者：张灿 ZHANG Can(School of Mathematics and Statistics,Wuhan University,Wuhan Hubei 430072,China)

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《控制理论与应用》2022年第9期1594-1600,共7页Control Theory & Applications

基　　金：国家自然科学基金项目(11971363);武汉大学青年学术团队建设项目(413100085)资助.

摘　　要：在前期工作[4-7]中,笔者证明当观测集是Lebesgue正可测集时,具有实解析系数抛物方程的能观性不等式成立.在这些工作中,笔者主要用到此类偏微分方程的解在正可测集上的定量估计式.在这篇文章中,将运用文献[19]的结论,建立有界区域上具有非实解析系数扩散方程在时空区域Lebesgue可测集上的能观性不等式.作为应用,本文将给出相应的时间或范数最优控制问题的bang-bang性.In our earlier works[4-7],we have proved observability inequalities from measurable sets hold for solutions of parabolic-type partial differential equations with real analytic coefficients in bounded domains.In these works,we have mainly utilized the propagation estimate of smallness for real analytic functions,and a telescoping series method.In the present paper,we shall establish the observability and controllability on measurable subsets in space and time variables for diffusion equations in bounded domains,without real analyticity assumptions on diffusion coefficients.As applications,we shall show bang-bang properties of time and norm optimal control problems governed by diffusion equations.

关 键 词：能观性不等式 零能控性 可测集 时间最优控制 

分 类 号：O232[理学—运筹学与控制论] O175[理学—数学]