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<p>In this paper, the authors study the problem of distributed Nash equilibrium seeking of <i>N</i>-player games with high-order integrator dynamics subject to disturbances generated by an uncertain exosystem. Similar problems have been studied for disturbances with an exactly known exosystem. Compared with the existing results of high-order integrator dynamics, which can only handle sinusoidal disturbances with known frequencies, this paper aims to handle multi-tone disturbances with unknown frequencies by introducing an adaptive control technique to estimate the unknown frequencies. Technically, when the exosystem is known, the disturbance can be dealt with by the Luenburger observer. In contrast, the Luenburger observer cannot deal with an uncertain exosystem. The authors combine the internal model design and some adaptive control technique to solve the proposed problem. Further, the authors also establish the sufficient condition to guarantee the convergence of the estimated unknown frequencies to the actual values of these frequencies. Two examples are given to verify the proposed algorithm.</p>

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Distributed Nash Equilibrium Seeking with Disturbances of Unknown Frequencies for High-Order Integrators over Jointly Strongly Connected Switching Networks

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Xiongnan He,
  • Jie Huang

摘要

In this paper, the authors study the problem of distributed Nash equilibrium seeking of N-player games with high-order integrator dynamics subject to disturbances generated by an uncertain exosystem. Similar problems have been studied for disturbances with an exactly known exosystem. Compared with the existing results of high-order integrator dynamics, which can only handle sinusoidal disturbances with known frequencies, this paper aims to handle multi-tone disturbances with unknown frequencies by introducing an adaptive control technique to estimate the unknown frequencies. Technically, when the exosystem is known, the disturbance can be dealt with by the Luenburger observer. In contrast, the Luenburger observer cannot deal with an uncertain exosystem. The authors combine the internal model design and some adaptive control technique to solve the proposed problem. Further, the authors also establish the sufficient condition to guarantee the convergence of the estimated unknown frequencies to the actual values of these frequencies. Two examples are given to verify the proposed algorithm.