TY - JOUR

T1 - An example in linear quadratic optimal control

AU - Weiss, George

AU - Zwart, Hans

N1 - Funding Information:
This paper was written during a visit of the first author to the University of Twente, supported by the Faculty of Applied Mathematics. The authors are grateful to Ruth F. Curtain and Martin Weiss for discussions on the subject. In the early stages of writing this paper, we have had useful e-mail exchanges on the subject with Roberto Triggiani and Irena Lasiecka.

PY - 1998/4/16

Y1 - 1998/4/16

N2 - We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme simplicity, this example has all the unexpected features discovered recently by O. Staffans (and also by M. Weiss and G. Weiss). More precisely, in the formula linking the optimal feedback operator to the optimal cost operator, as well as in the Riccati equation, the weighting operator of the input has to be replaced by another operator, which can be derived from the spectral factorization of the Popov function.

AB - We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme simplicity, this example has all the unexpected features discovered recently by O. Staffans (and also by M. Weiss and G. Weiss). More precisely, in the formula linking the optimal feedback operator to the optimal cost operator, as well as in the Riccati equation, the weighting operator of the input has to be replaced by another operator, which can be derived from the spectral factorization of the Popov function.

KW - Infinite-dimensional systems

KW - Linear quadratic optimal control

KW - Riccati equations

KW - Shift semigroups

KW - Spectral factorization

UR - http://www.scopus.com/inward/record.url?scp=0346838145&partnerID=8YFLogxK

U2 - 10.1016/S0167-6911(97)00126-6

DO - 10.1016/S0167-6911(97)00126-6

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AN - SCOPUS:0346838145

SN - 0167-6911

VL - 33

SP - 339

EP - 349

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 5

ER -