Commutant Lifting for Optimal Control of Time-Varying Systems (Communications in Mathematical Research, 2021)
This paper uses the commutant lifting theorem for representations ofthe 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 existenceof an optimal controller.
Keywords: optimal control; four block problem; commutant lifting; time-varying; nest algebra.