含终端等式约束LQ时变控制器设计的新方法  

A new approach to LQ time-varying controllers with terminal equality constraints

作　　者：谭述君[1,2] 吴志刚[1,2] 钟万勰[2] 

机构地区：[1]大连理工大学航空航天学院,大连116024 [2]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《中国科学：物理学、力学、天文学》2013年第4期549-556,共8页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:11002032;11072044);新世纪优秀人才支持计划(编号:NCET-11-0054);中央高校基本科研业务费专项资金(编号:DUT12LK25)资助项目

摘　　要：对于LQ终端约束控制问题,利用所引入的Lagrange乘子是常数的本质,构造了新的两区段形式的终端控制器,避免了传统控制器在靠近终端区段时反馈增益矩阵过大、甚至奇异的缺点,而且两个区段的控制律都具有反馈-前馈结构;对求解终端控制器问题的变分原理做了改进,分析了新变分式中的软约束项与反馈增益矩阵之间的联系,指出它对于构造反馈结构的控制器,尤其是对最小能量控制问题,具有重要的意义.进一步,利用区段混合能理论中的能量矩阵,构造了终端控制器的矩阵Riccati微分方程组的闭合解.最后,通过求解一个航天器交会最优控制问题,检验了本文所设计的LQ终端约束控制器的有效性及优越性.A two-interval LQ terminal controller is constructed by using the fact that the Lagrange multiplier of the variational principle is a constant. The new terminal controller not only overcomes the drawbacks that the feedback gains of conventional LQ terminal controllers tend to infinity when close to the final time, but also keeps a feedback- feedforward structure. The variational principle for the LQ terminal control problem is also improved by adding a soft constraint. Relation between the ＂soft term＂ and the feedback gain is presented that the ＂soft term＂ is an enhancer to improve the performance of the controller, especially for minimum energy control problems. Further more, based on the interval mixed energy theory, closed form solutions of generalized Riccati transformation matrices are given. Advantages of the proposed two-interval terminal controller and effectiveness of the closed-form solutions are verified by numerical examples of an optimal rendezvous problem of spacecrafts.

关 键 词：LQ终端控制器 奇异性 最优交会对接问题 区段混合能 精细积分方法 

分 类 号：O231[理学—运筹学与控制论]