Perturbation of multivariable linear quadratic systems with jump parameters

Considers the problem of the perturbation of a class of linear quadratic systems where the change from one structure (for the dynamics and costs) to another is governed by a finite-state Markov process. The problem above leads to the analysis of some perturbed linearly coupled sets of Riccati equati...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2001-10, Vol.46 (10), p.1666-1671
Main Authors: El Azouzi, R., Abbad, M., Altman, E.
Format: Article
Language:English
Subjects:
Control design
Costs
Dynamical systems
Dynamics
Linear quadratic
Linear systems
Markov processes
Mathematical analysis
Optimal control
Optimization
Perturbation methods
Production management
Riccati equation
Riccati equations
State-space methods
Taylor series
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Summary:Considers the problem of the perturbation of a class of linear quadratic systems where the change from one structure (for the dynamics and costs) to another is governed by a finite-state Markov process. The problem above leads to the analysis of some perturbed linearly coupled sets of Riccati equations. We show that the matrix obtained as the solution of the equations, which determines the optimal value and control, has a Taylor expansion in the perturbation parameter. We compute explicitly the terms of this expansion.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.956069