On the Pareto Control and No-Regret Control for Distributed Systems with Incomplete Data

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 as...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on control and optimization Vol. 42; no. 4; pp. 1167 - 1184
Main Authors Nakoulima, O., Omrane, A., Velin, J.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2003
Subjects
Hilbert space
Mathematics
Optimization and Control
Pareto optimum
cost function
systems with incomplete data
low-regret control
no-regret control
quadratic perturbation
Pareto control
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0363-0129
1095-7138
DOI:10.1137/S0363012900380188