Continuous-time distributed Nash equilibrium seeking algorithms for non-cooperative constrained games

• DOI: 10.1016/j.automatica.2021.109535
• Publication Date: 2021-02-26T19:00:07Z
• Authors: Yao Zou; Bomin Huang; Ziyang Meng; Wei Ren
• Keywords: Operator (biology)

Abstract This paper studies the Nash equilibrium seeking problem for non-cooperative games subject to set and nonlinear inequality constraints . The cost function for each player and the constrained function are determined by all the players’ decision variables. Each player is assigned a constrained set while all the players are subject to a coupling nonlinear inequality constraint. A continuous-time distributed seeking algorithm using local information interaction is proposed, where the players deliver/receive information unidirectionally over a directed network. In particular, a distributed observer is first introduced for each player to estimate all the others’ decision variables. Then, by using these estimates, a seeking algorithm is synthesized with a projection operator. Based on the time-scale separation approach, it is shown that the proposed continuous-time distributed seeking algorithm guarantees the convergence of the strategy profile to an arbitrarily small neighborhood of the generalized Nash equilibrium satisfying a KKT condition. An illustrative example is finally presented to validate the theoretical results.