Nash equilibrium seeking in potential games with double-integrator agents
For researchers in multi-agent control and game theory, this work provides a novel connection between port-Hamiltonian systems and potential games, enabling distributed Nash equilibrium seeking with double-integrator dynamics.
The paper establishes an equivalence between a constrained multi-agent control problem in the port-Hamiltonian framework and an exact potential game, and proposes a distributed gradient-based control law that steers double-integrator agents to Nash equilibria. The approach uses virtual couplings to shape transient behavior and reachable equilibria.
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 behaviour (i.e., the convergence) and, ideally, the set of reachable equilibria.