Technical Communique: An equivalence result in linear-quadratic theory

Authors:
W. A. Van Den Broek;J. C. Engwerda;J. M. Schumacher
Affiliations:
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, Netherlands;Department of Econometrics and Operations Research, Center for Economic Research (CentER), Tilburg University, P.O. Box 90153, 5000 LE Tilburg, Netherlands;Department of Econometrics and Operations Research, Center for Economic Research (CentER), Tilburg University, P.O. Box 90153, 5000 LE Tilburg, Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2003

Citing 2
Cited 1

Asymptotic analysis of linear feedback Nash equilibria in nonzero-sum linear-quadratic differential games

Journal of Optimization Theory and Applications
Paper: The time-invariant linear-quadratic optimal control problem

Automatica (Journal of IFAC)

Technical communique: A result on output feedback linear quadratic control

Automatica (Journal of IFAC)

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Abstract

We consider the zero-endpoint infinite-horizon LQ problem. We show that the existence of an optimal policy in the class of feedback controls is a sufficient condition for the existence of a stabilizing solution to the algebraic Riccati equation. This result is shown without assuming positive definiteness of the state weighting matrix. The feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria both in a deterministic and stochastic context.