TY - GEN
T1 - Fixed-Time Seeking and Tracking of Time-Varying Nash Equilibria in Noncooperative Games
AU - Poveda, Jorge I.
AU - Krstic, Miroslav
AU - Basar, Tamer
N1 - Publisher Copyright:
© 2022 American Automatic Control Council.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
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U2 - 10.23919/ACC53348.2022.9867782
DO - 10.23919/ACC53348.2022.9867782
M3 - Conference contribution
AN - SCOPUS:85138492270
T3 - Proceedings of the American Control Conference
SP - 794
EP - 799
BT - 2022 American Control Conference, ACC 2022
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2022 American Control Conference, ACC 2022
Y2 - 8 June 2022 through 10 June 2022
ER -