TY - GEN
T1 - Local First-Order Algorithms for Constrained Nonlinear Dynamic Games
AU - Di, Bolei
AU - Lamperski, Andrew
N1 - Publisher Copyright:
© 2020 AACC.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/7
Y1 - 2020/7
N2 - This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact over time. They model a wide range of applications include economics, defense, and energy systems. We show how to exploit the temporal structure in projected gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms converge locally to open-loop Nash equilibria (OLNE) at linear rates. Furthermore, we extend a stagewise Newton method to find a local feedback policy around an OLNE. In the special case of linear dynamics and polyhedral constraints, we show that this local feedback controller is an approximate feedback Nash equilibrium.
AB - This paper presents algorithms for non-zero sum nonlinear constrained dynamic games with full information. Such problems emerge when multiple players with action constraints and differing objectives interact over time. They model a wide range of applications include economics, defense, and energy systems. We show how to exploit the temporal structure in projected gradient and Douglas-Rachford (DR) splitting methods. The resulting algorithms converge locally to open-loop Nash equilibria (OLNE) at linear rates. Furthermore, we extend a stagewise Newton method to find a local feedback policy around an OLNE. In the special case of linear dynamics and polyhedral constraints, we show that this local feedback controller is an approximate feedback Nash equilibrium.
UR - http://www.scopus.com/inward/record.url?scp=85089566839&partnerID=8YFLogxK
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U2 - 10.23919/ACC45564.2020.9147602
DO - 10.23919/ACC45564.2020.9147602
M3 - Conference contribution
AN - SCOPUS:85089566839
T3 - Proceedings of the American Control Conference
SP - 5358
EP - 5363
BT - 2020 American Control Conference, ACC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2020 American Control Conference, ACC 2020
Y2 - 1 July 2020 through 3 July 2020
ER -