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Dissipative Control Systems and Disturbance Attenuation for Nonlinear H ∞ Problems

Frankowska, Halina; Quincampoix, Marc (1999), Dissipative Control Systems and Disturbance Attenuation for Nonlinear H ∞ Problems, Applied Mathematics and Optimization, 40, 2, p. 163-181. http://dx.doi.org/10.1007/s002459900120

Type
Article accepté pour publication ou publié
Date
1999
Journal name
Applied Mathematics and Optimization
Volume
40
Number
2
Publisher
Springer
Pages
163-181
Publication identifier
Metadata
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Author(s)
Frankowska, Halina
Quincampoix, Marc
Abstract (EN)
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 ∞ problem from contingent formulation of Isaacs' equation.
Subjects / Keywords
Isaacs' equation; H∞ problem; Contingent and viscosity solutions to PDEs