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.
Type de document :
Rapport
RR-3816, INRIA. 1999
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Soumis le : mercredi 24 mai 2006 - 11:04:48
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:24:54

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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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