Distributed Nash equilibrium seeking for aggregative games with coupled constraints

Abstract

In this paper, we study a distributed continuous-time design for aggregative games with coupled constraints in order to seek the generalized Nash equilibrium by a group of agents via simple local information exchange. To solve the problem, we propose a distributed algorithm based on projected dynamics and non-smooth tracking dynamics, even for the case when the interaction topology of the multi-agent network is time-varying. Moreover, we prove the convergence of the non-smooth algorithm for the distributed game by taking advantage of its special structure and also combining the techniques of the variational inequality and Lyapunov function.

Distributed algorithm design for aggregative games of disturbed multiagent systems over weight‐balanced digraphs

“…The exogenous disturbance results that most of existing distributed algorithms cannot ensure the multiagent system converge to the GNE of the game. Moreover, the communication among players is depicted by weight‐balanced digraphs, which extend undirected graphs considered by most of existing results about aggregative games . Besides, unlike the differential games that are known as dynamic games (see the work of Başar and Olsder for details), the aggregative games considered here are static games, where the cost functions of all players are independent of the derivatives of decisions and the transient trajectories given by algorithms, though exogenous disturbances are involved for players.…”

“…Remark 1. Different from most of aggregative games, 11,[15][16][17][18][19][20] our formulation involves exogenous disturbances for players. The exogenous disturbance results that most of existing distributed algorithms cannot ensure the multiagent system (7) converge to the GNE of the game.…”

“…Moreover, Liang et al presented a distributed continuous‐time algorithm for aggregative games with local strategy constraints, and Paccagnan et al proposed a distributed discrete‐time algorithm for quadratic aggregative games with linear inequality coupling constraints. Besides, Liang et al studied a distributed algorithm for aggregative games with local strategy constraints and linear equality coupling constraints. Additionally, Grammatico gave a model‐free dynamic control law for aggregative games.…”

“…Moreover, Gharesifard and Cortés 27 pointed out that a convergent algorithm over undirected graphs may be divergent for some digraphs. It is worthwhile mentioning that many distributed GNE seeking algorithms depend on the undirected graphs such as those in other works, 11,[15][16][17][18][19][20] while there are few results about aggregative games over directed graphs.…”

“…(i) We formulate the aggregative games of multiagent systems with linear coupling constraints and weight-balanced digraphs, where all players have first-order dynamics and are influenced by exogenous disturbances. The considered problem can be viewed as extensions of some well-known problems, including the aggregative games discussed in other works 11,[15][16][17][18][19][20] by adding disturbed multiagent systems over weight-balanced digraphs and distributed control and optimization of multiagent system investigated in the works of Lin and Ren 6 and Deng et al 8 by considering game concerns. Without involving exogenous disturbances and weight-balanced digraphs, many existing distributed GNE seeking algorithms cannot be applied to our problem.…”