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GNE seeking in games with passive dynamic agents via inexact-penalty methods

In this paper, we consider a network of autonomous agents with passive linear time-invariant dynamics involved in a game with coupled constraints. In such networked scenarios, agents have to make decisions compatible with seeking a generalized Nash equilibrium (GNE), while using networked information and satisfying the constraints. Existing methods are developed for multi-integrator agents only and furthermore, ensure the satisfaction of coupled constraints in steady-state only. We propose an inexact-penalty dynamics for passive LTI agents and show that it converges to an ϵ -GNE while ensuring the coupled constraints are met throughout the evolution of the agents’ dynamics, not only in steady-state. Our scheme is developed for both the full-decision information setting and the partial-decision one. In the partial-information setting, each agent makes its decision based on a dynamic estimate of the others’ states, updated by local communication with its neighbours, which offsets the lack of global information. Applications to optical networks are provided.