Nash equilibrium seeking in potential games with double-integrator agents

Conference paper (2019)

Authors

F. Fabiani University of Pisa, Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Andrea Caiti University of Pisa
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
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Published Date

2019

Language

English

Reuse Rights

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

In this paper, we show the equivalence between a constrained, multi-agent control problem, modeled within the port-Hamiltonian framework, and an exact potential game. Specifically, critical distance-based constraints determine a network of double-integrator agents, which can be represented as a graph. Virtual couplings, i.e., pairs of spring-damper, assigned to each edge of the graph, allow to synthesize a distributed, gradient-based control law that steers the network to an invariant set of stable configurations. We characterize the points belonging to such set as Nash equilibria of the associated potential game, relating the parameters of the virtual couplings with the equilibrium seeking problem, since they are crucial to shape the transient behavior (i.e., the convergence) and, ideally, the set of achievable equilibria.