广义系统奇异LQ问题的解法  

The Singular LQ Problems for Generalized Systems

作　　者：张春蕊[1] 

机构地区：[1]东北林业大学

出　　处：《东北林业大学学报》1998年第3期29-33,共5页Journal of Northeast Forestry University

摘　　要：文章以矩阵理论为工具，研究了广义系统奇异二次指标最优控制问题（简称广义系统奇异ＬＱ问题）的解法。讨论了半无限区间上广义系统奇异ＬＱ问题的解及此问题与正常状态空间奇异ＬＱ问题的内在联系，并得出结论：在广义系统脉冲能控的条件下，其奇异ＬＱ问题等价于一个正常状态空间的奇异ＬＱ问题或是一个非奇异ＬＱ问题。在对系统附加一定的条件下，其解是唯一的，并且最优闭环是渐近稳定的。同时利用系统矩阵提供的信息给出广义系统脉冲能控的充要条件是ＲａｎｋＥＯ９ＡＢＥ＝ｎ＋ｒ．Based on the theories of matrix, linear quadratic optimal regular problems for generalized systems was studied. The problems in infinite half-interval were discussed, and the relations between the problems and the normal LQ problems for linear time-invariant systems was given. Under the equivalence principle of optimal controls, the existence and uniqueness of the solution were also discussed. The conclusion was obtained: if the systems are regular the singular LQ problem is equivalent a singular LQ problem or a non-singular LQ problem for normal linear systems,and if some conditions are added the solution of the singular LQ problem is unique, and the optimal closed-loop systems are asymptotiallytable. At the same time another conclusion was obtained: the impulsive modes of the system are controllable if and only if Rank EO9 ABE=n+r.

关 键 词：广义系统 奇LQ问题 脉冲能控 最优控制 

分 类 号：O232[理学—运筹学与控制论]