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

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

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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.
Original languageEnglish
Place of PublicationTilburg
PublisherMacroeconomics
Number of pages12
Volume2000-38
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper
Volume2000-38

Fingerprint

Linear systems
Controllers
State feedback
Uncertainty

Keywords

  • Linear uncertain systems
  • game theory
  • algebraic Riccati equations

Cite this

van den Broek, W. A., Engwerda, J. C., & Schumacher, J. M. (2000). A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances. (CentER Discussion Paper; Vol. 2000-38). Tilburg: Macroeconomics.
van den Broek, W.A. ; Engwerda, J.C. ; Schumacher, J.M. / A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances. Tilburg : Macroeconomics, 2000. (CentER Discussion Paper).
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van den Broek, WA, Engwerda, JC & Schumacher, JM 2000 'A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances' CentER Discussion Paper, vol. 2000-38, Macroeconomics, Tilburg.

A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances. / van den Broek, W.A.; Engwerda, J.C.; Schumacher, J.M.

Tilburg : Macroeconomics, 2000. (CentER Discussion Paper; Vol. 2000-38).

Research output: Working paperDiscussion paperOther research output

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AU - Schumacher, J.M.

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PY - 2000

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N2 - 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.

AB - 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.

KW - Linear uncertain systems

KW - game theory

KW - algebraic Riccati equations

M3 - Discussion paper

VL - 2000-38

T3 - CentER Discussion Paper

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

PB - Macroeconomics

CY - Tilburg

ER -

van den Broek WA, Engwerda JC, Schumacher JM. A Game Theoretic Approach to Linear Systems with L2-bounded Disturbances. Tilburg: Macroeconomics. 2000. (CentER Discussion Paper).