TY - JOUR
T1 - Commutant Lifting for Optimal Control of Time-Varying Systems
AU - Liu , Liu
AU - Lu , Yufeng
JO - Communications in Mathematical Research 
VL - 3
SP - 252
EP - 264
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19048.html
KW - optimal control, four block problem, commutant lifting, time-varying,
nest algebra.
AB - <p style="text-align: justify;">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.</p>