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
TypeArticle accepté pour publication ou publié
Journal nameApplied Mathematics and Optimization
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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 / KeywordsIsaacs' equation; H∞ problem; Contingent and viscosity solutions to PDEs
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