1. On the Pareto control and no-regret control for distributed systems with incomplete data
- Author
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J. Velin, Ousseynou Nakoulima, A. Omrane, Centre de Recherche en Economie, Gestion, Modélisation et Informatique Appliquée (CEREGMIA), Université des Antilles et de la Guyane (UAG), and Laboratoire de Mathématiques Informatique et Applications (LAMIA)
- Subjects
low-regret control ,quadratic perturbation ,0209 industrial biotechnology ,Control and Optimization ,Applied Mathematics ,Distributed computing ,010102 general mathematics ,Pareto principle ,Pareto control ,systems with incomplete data ,Regret ,02 engineering and technology ,Missing data ,01 natural sciences ,no-regret control ,010101 applied mathematics ,020901 industrial engineering & automation ,Singularity ,Quadratic equation ,cost function ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,0101 mathematics ,Mathematics - Abstract
International audience; We discuss the control of distributed systems with incomplete data following the notion of no-regret control (or, equivalently, Pareto control) used by Lions in [C. R. Acad. Sci. Paris Ser. I Math., 302 (1986), pp. 223-227] and [C. R. Acad. Sci. Paris Ser. I Math., 302 (1992), pp. 1253-1257]. We associate with the no-regret control a sequence of low-regret controls defined by a quadratic perturbation previously used by Nakoulima, Omrane, and Velin in [C. R. Acad. Sci. Paris Ser. I Math., 330 (2000), pp. 801-806]. In the first part, we prove that the perturbed system corresponds to a sequence of standard control problems and converges to the no-regret (or Pareto) control for which we obtain a singular optimality system. We give also some applications. In the second part, we show how the method can be extended to the evolution case. Equations of parabolic type, Petrowsky type, or hyperbolic type are considered.
- Published
- 2004
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