Fixed-Time Seeking and Tracking of Time-Varying Nash Equilibria in Noncooperative Games

Jorge I. Poveda, Miroslav Krstic, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the solution of time-varying Nash equilibrium seeking and tracking problems in non-cooperative games via nonsmooth, model-based and model-free algorithms. Specifically, for potential and non-potential games, we derive tracking bounds for the actions of the players with respect to the Nash Equilibrium Trajectory (NET) of the game using the property of fixed-time input-to-state stability. We show that, in the model-based case, traditional pseudo-gradient flows achieve only exponential tracking with a residual error that is proportional to the time-variation of the NET. In contrast, exact and fixed-time tracking can be achieved by using nonsmooth dynamics with discontinuous vector fields. For continuous but non-Lipschitz dynamics, we show that the residual tracking error can be dramatically decreased whenever the learning gains of the dynamics exceed a particular threshold. In the model-free case, we derive similar semi-global practical input-to-state stability bounds using multi-time scale tools for nonsmooth systems.

Original languageEnglish (US)
Title of host publication2022 American Control Conference, ACC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages794-799
Number of pages6
ISBN (Electronic)9781665451963
DOIs
StatePublished - 2022
Externally publishedYes
Event2022 American Control Conference, ACC 2022 - Atlanta, United States
Duration: Jun 8 2022Jun 10 2022

Publication series

NameProceedings of the American Control Conference
Volume2022-June
ISSN (Print)0743-1619

Conference

Conference2022 American Control Conference, ACC 2022
Country/TerritoryUnited States
CityAtlanta
Period6/8/226/10/22

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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