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Perturbation of linear quadratic systems with jump parameters and hybrid controls

Author

Listed:
  • Rachid El Azouzi
  • Mohammed Abbad
  • Eitan Altman

Abstract

We consider the problem of the perturbation of a class of linear-quadratic differential games with piecewise deterministic dynamics, where the changes from one structure (for the dynamics) to another are governed by a finite-state Markov process. Player 1 controls the continuous dynamics, whereas Player 2 controls the rate of transition for the finite-state Markov process; both have access to the states of both processes. Player 1 wishes to minimize a given quadratic performance index, while player 2 wishes to maximize or minimize the same quantity. The problem above leads to the analysis of some linearly coupled set of quadratic equations (Riccati equations). We obtain a Taylor expansion in the perturbation for the solution of the equation for a fixed stationary policy of the player 2. This allows us to solve the game or team problem as a function of the perturbation. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Rachid El Azouzi & Mohammed Abbad & Eitan Altman, 2000. "Perturbation of linear quadratic systems with jump parameters and hybrid controls," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 399-417, August.
    • Handle: RePEc:spr:mathme:v:51:y:2000:i:3:p:399-417
    DOI: 10.1007/s001860000050
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