时变系统线性二次型问题:无约束条件时的一般结果和有控制能量约束条件时的讨论

Linear Quadratic Problem for Time-Varying Systems:the Cases without Constraints and with the Control Energy Constraint

本文中我们首先对无约束条件时的有限时间区间上时变系统线性二次型（FHLQ）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HLLQ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。

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 (Them 2) .We prove thatfor the FH-LQ problems the statements of finite infimum and achieved finite infimum are equivalent to each other(Them 1).Basing on this we derive some new conditions for the regular case (Them 3) .Finally,we discuss the FH-LQ problem with con-trol energy constraint via an approach called 'lossless S-procedure.