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Title: Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems

Abstract

We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H{sup {infinity}} problem from contingent formulation of Isaacs' equation.

Authors:
 [1];  [2]
  1. CNRS and Centre de Recherches VJC, Universite Paris-Dauphine, Place du Marechal de Lattre de Tassigny, 75775 Paris cedex 16 (France)
  2. Departement de Mathematiques, Universite de Bretagne Occidentale, Avenue Le Gorgeu, B.P. 809, 29285 Brest cedex (France)
Publication Date:
OSTI Identifier:
21067544
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 40; Journal Issue: 2; Other Information: DOI: 10.1007/s002459900120; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTENUATION; CONTROL SYSTEMS; CONTROL THEORY; DISTURBANCES; FEEDBACK; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS

Citation Formats

Frankowska, H., and Quincampoix, M. Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems. United States: N. p., 1999. Web. doi:10.1007/S002459900120.
Frankowska, H., & Quincampoix, M. Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems. United States. doi:10.1007/S002459900120.
Frankowska, H., and Quincampoix, M. Wed . "Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems". United States. doi:10.1007/S002459900120.
@article{osti_21067544,
title = {Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems},
author = {Frankowska, H. and Quincampoix, M.},
abstractNote = {We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H{sup {infinity}} problem from contingent formulation of Isaacs' equation.},
doi = {10.1007/S002459900120},
journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 2,
volume = 40,
place = {United States},
year = {1999},
month = {9}
}