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Volume 28, Issue 3
Commutant Lifting for Optimal Control of Time-Varying Systems

Liu Liu & Yufeng Lu

Commun. Math. Res., 28 (2012), pp. 252-264.

Published online: 2021-05

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  • Abstract

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.

  • Keywords

optimal control, four block problem, commutant lifting, time-varying, nest algebra.

  • AMS Subject Headings

47B35, 47B47

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-28-252, author = {Liu and Liu and and 15973 and and Liu Liu and Yufeng and Lu and and 18528 and and Yufeng Lu}, title = {Commutant Lifting for Optimal Control of Time-Varying Systems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {3}, pages = {252--264}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19048.html} }
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 -

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.

Liu Liu & Yufeng Lu. (2021). Commutant Lifting for Optimal Control of Time-Varying Systems. Communications in Mathematical Research . 28 (3). 252-264. doi:
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