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

Abstract

Summary In this paper, an aggregative game of multiagent systems over weight‐balanced digraphs is studied, where the decisions of all players are coupled by linear constraints. Different from the well‐known aggregative games, the dynamics of players are disturbed first‐order linear systems in our problem. In order to seek the variational generalized Nash equilibrium (GNE) of the game, a distributed algorithm is developed via gradient descent, internal model, and dynamic average consensus, where the gradient is for seeking the variational GNE, the internal model is for rejecting the exogenous disturbances, and the dynamic average consensus is for estimating the aggregate of the decisions of all players. The exponential convergence of the algorithm to the variational GNE is analyzed by constructing suitable Lyapunov functions. Finally, the effectiveness of our method is illustrated via two examples.

Consensus‐based and extremum seeking methods for distributed generalized nash equilibrium

“…Before presenting our algorithms, some assumptions are needed, which are widely used in References 7,8,29, and 30.…”

“…Distributed generalized Nash equilibrium (GNE) seeking problems are explored in this article. For the constrained games, some work has been done (e.g., see References 1‐11 and references cited therein). Reference 1 considered the game with affine constraints and designed a distributed GNE seeking algorithm by employing forward‐backward operator splitting methods.…”

Nash Equilibrium Seeking for General Linear Systems with Disturbance Rejection

“…Aggregative games, as a special class of noncooperative games with cost functions depending on player's own strategy and the aggregation of strategies of all players, have attracted an increasing interest (see [14], [17], [19], [24], [29], [30] and the references therein). Some work therein focuses on aggregative games with complex dynamic systems including Euler-Lagrange systems [24], nonlinear systems [28].…”

“…Some work therein focuses on aggregative games with complex dynamic systems including Euler-Lagrange systems [24], nonlinear systems [28]. Furthermore, the competition among distributed energy resources in electricity market can be modeled as aggregative games [24], [29]. The output power of each generation system, as the strategy, is driven by the turbine-generator dynamics, which is a high-order linear system.…”

“…Although various NE seeking algorithms have been developed, these algorithms may fail to seek NE in the presence of disturbances. Recently, some work has focused on the distributed NE seeking of multi-agent systems with disturbances which may be generated by exosystems or just assumed to be bounded [26], [28], [29], [31]. In [26], [29], dynamic compensators were designed based on the internal models for integrator-type agents with the known models of disturbances.…”