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


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.
Number of pages6
ISBN (Electronic)9781665451963
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
ISSN (Print)0743-1619


Conference2022 American Control Conference, ACC 2022
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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