A framework for receding-horizon control in infinite-horizon aggregative games

TL;DR

This paper introduces a new framework for receding-horizon control in infinite-horizon aggregative games, analyzing strategic behavior and convergence to equilibrium under heterogeneous constraints using Lyapunov stability and set-valued dynamical systems.

Contribution

It proposes a novel modeling framework and equilibrium concept for infinite-horizon aggregative games, with convergence analysis and a distributed control example.

Findings

Convergence of the receding horizon map to a periodic equilibrium is established.

The framework is robust to initial conditions and real-time variations.

Simulation demonstrates effective distributed control for data routing.

Abstract

A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary conditions are derived for convergence of a receding horizon map to a periodic equilibrium of the aggregative game. This result is achieved for any (feasible) initial condition, thus ensuring implicit adaptivity of the proposed control framework to real-time variations in the number and parameters of players. Design and implementation of the proposed control strategy are discussed and an example of distributed control for data routing is presented, evaluating its performance in simulation.