引用本文:陈阳舟.时变系统线性二次型问题：无约束条件的一般结果和有控制能量约束条件的讨论[J].控制理论与应用,1999,16(4):474~477.[点击复制]
Chen Yangzhou.Linear Quadratic Problem for Time-Varying Systems:the Cases without Constraints and with the Control Energy Constraint[J].Control Theory and Technology,1999,16(4):474~477.[点击复制]
时变系统线性二次型问题：无约束条件的一般结果和有控制能量约束条件的讨论
Linear Quadratic Problem for Time-Varying Systems:the Cases without Constraints and with the Control Energy Constraint
摘要点击 1252  全文点击 518  投稿时间：1995-09-27  修订日期：1997-10-10
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DOI编号  
  1999,16(4):474-477
中文关键词  线性二次型问题  有限时区上的时变系统  正则与奇异问题  控制能量有界  不亏损S-过程
英文关键词  linear-quadratic problem  finite-horizon time-varying systems  singular and regular problems  boundary control energy  lossless S-procedure.
基金项目  
作者单位
陈阳舟  
中文摘要
      本文中我们首先对无约束条件的有限时间区间上时变系统线性二次型（FH-LQ）问题进行了分类，并给出了问题属于每一类的充分必要条件（定理2）.其次证明了对于(FH-LQ)问题其下确界有限与其可达是等价的（定理1）.在此基础上给出了问题为正则的一些新的条件（定理3）.最后，我们通过新的途径讨论了有控制能量约束时的FH-LQ问题.
英文摘要
      In the paper,we first make a classification for general finite-horizon time-varying linear quadratic (FH-LQ) problems and give out a necessary and sufficient condition on which the problem belongs to some class(them2).We prove that for the FH-LQ problems the statements of finite infimum and achieved finite infimum are equivalent to each other(Them1).Basing on this we derive some new conditions for the regular case(Them3).Finally, we discuss the FH-LQ problem with control energy constraint via approach called “lossless S-procedure”.