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We propose an integral Nash equilibrium seeking control (I-NESC) law whichsteers the multi-agent system composed of a special class of linear agents tothe neighborhood of the Nash equilibrium in noncooperative strongly monotonegames. First, we prove that there exist parameters of the integral controllersuch that the system converges to the Nash equilibrium in the full-informationcase, in other words, without the parameter estimation scheme used in extremumseeking algorithms. Then we prove that there exist parameters of the I-NESCsuch that the system converges to the neighborhood of the Nash equilibrium inthe limited information case where parameter estimation is used. We provide asimulation example that demonstrates that smaller perturbation frequencies andamplitudes are needed to attain similar convergence speed as the existingstate-of-the-art algorithm.

An integral Nash equilibrium control scheme for a class of multi-agent linear systems