Commutant Lifting for Optimal Control of Time-varying Systems  

作　　者：Liu LIU Lu YU-FENG 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116021

出　　处：《Communications in Mathematical Research》2012年第3期252-264,共13页数学研究通讯（英文版）

基　　金：The NSF (10971020) of China

摘　　要：This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.This paper uses the commutant lifting theorem for representations of the nest algebra to deal with the optimal control of infinite dimensional linear time- varying systems. We solve the model matching problem and a certain optimal feedback control problem, each of which corresponds with one type of four-block problem. We also obtain a new formula for the optimal performance and prove the existence of an optimal controller.

关 键 词：optimal control four block problem commutant lifting TIME-VARYING nest algebra 

分 类 号：O177.1[理学—数学] TM571.62[理学—基础数学]