Premium
Noncooperative Model Predictive Control for Affine‐Quadratic Games
Author(s) -
Stieler Marleen,
Baumann Michael H.,
Grüne Lars
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800036
Subject(s) - nash equilibrium , mathematical economics , uniqueness , best response , affine transformation , mathematical optimization , convergence (economics) , model predictive control , mathematics , epsilon equilibrium , optimal control , computer science , control (management) , economics , artificial intelligence , pure mathematics , mathematical analysis , economic growth
Nash strategies are a natural solution concept in noncooperative game theory because of their ‘stable’ nature: If the other players stick to the Nash strategy it is never beneficial for one player to unilaterally change his or her strategy. In this sense, Nash strategies are the only reliable strategies. The idea to perform and analyze Model Predictive Control (MPC) based on Nash strategies instead of optimal control sequences is appealing because it allows for a systematic handling of noncooperative games, which are played in a receding horizon manner. In this paper we extend existence and uniqueness results on Nash equilibria for affine‐quadratic games. For this class of games we moreover state sufficient conditions that guarantee trajectory convergence of the MPC closed loop.