Data-Driven Spiking Control for Distributed $\varepsilon$-Nash Equilibrium Seeking
This paper studies how a feedback law synthesized directly from data can be realized by spiking control while retaining a game-theoretic performance guarantee. We consider distributed $\varepsilon$-Nash equilibrium (NE) seeking in network games played by linear dynamical agents with unknown models and exogenous disturbances. The pseudo-gradient of the game is treated as a regulated error, and local internal models account for signals generated by known exosystems. Robust linear matrix inequalities are then used to compute stabilizing analogue feedback gains directly from noisy local input-state data, without identifying the agent dynamics. To implement these gains using only fixed-weight spikes, we develop two spiking realizations. The first realization uses non-interacting leaky integrate-and-fire units, while the second permits reset coupling among the neuronal units. In both cases, a continuous auxiliary coordinate exposes the impulsive closed loop as the stable analogue system driven by a bounded implementation error. This representation yields forward completeness, Zeno-freeness, and an ultimate bound on the pseudo-gradient, subject to explicit event-processing conditions for the connected architecture. The bound implies that, after a finite transient, the agents' outputs constitute an $\varepsilon$-NE for every $\varepsilon$ above a finite threshold. A spacecraft formation reconfiguration example illustrates the data-driven synthesis, the two spiking realizations, and their practical equilibrium behavior.