Perturbation of Linear Quadratic Systems with Jump Parameters and Hybrid Controls - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports Year : 1999

Perturbation of Linear Quadratic Systems with Jump Parameters and Hybrid Controls

Mohammed Abbad
  • Function : Author
Eitan Altman
  • Function : Author
  • PersonId : 830042

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.
Fichier principal
Vignette du fichier
RR-3816.pdf (269.56 Ko) Télécharger le fichier

Dates and versions

inria-00072842 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00072842 , version 1

Cite

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

Share

Gmail Facebook Twitter LinkedIn More