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A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances

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  • Broek, W.A. van den
  • Engwerda, J.C.
  • Schumacher, J.M.

    (Tilburg University, Center for Economic Research)

Abstract

The aim of the present study is to construct a state feedback controller for a given linear system that minimizes the worst-case effect of an L2 -bounded disturbance. Our setting is different from the usual framework of H -theory in that we consider nonzero initial conditions. The situation is modeled in a game theoretical framework, in which the controller designer acts as a minimizing player, and the uncertainty as a maximizing player. We show that a saddle-point equilibrium exists and find an optimal controller.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2000-38.

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Date of creation: 2000
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Handle: RePEc:dgr:kubcen:200038

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Web page: http://center.uvt.nl

Related research

Keywords: Linear uncertain systems; game theory; algebraic Riccati equations;

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  1. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
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