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Perturbation of Linear Quadratic Systems with Jump Parameters and Hybrid Controls

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-stat- e 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 Equation). 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.
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https://hal.inria.fr/inria-00072842
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Submitted on : Wednesday, May 24, 2006 - 11:04:48 AM
Last modification on : Friday, February 4, 2022 - 3:18:26 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:24:54 PM

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  • HAL Id : inria-00072842, version 1

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Rachid El-Azouzi, Mohammed Abbad, Eitan Altman. Perturbation of Linear Quadratic Systems with Jump Parameters and Hybrid Controls. RR-3816, INRIA. 1999. ⟨inria-00072842⟩

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