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IEEE/CAA Journal of Automatica Sinica

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Maojiao Ye, Danhu Li, Qing-Long Han, and Lei Ding, "Distributed Nash Equilibrium Seeking for General Networked Games with Bounded Disturbances," IEEE/CAA J. Autom. Sinica,doi: 10.1109/JAS.2022.105428
 Citation: Maojiao Ye, Danhu Li, Qing-Long Han, and Lei Ding, "Distributed Nash Equilibrium Seeking for General Networked Games with Bounded Disturbances," IEEE/CAA J. Autom. Sinica,

# Distributed Nash Equilibrium Seeking for General Networked Games with Bounded Disturbances

##### doi: 10.1109/JAS.2022.105428
Funds:  This work was supported by the National Natural Science Foundation of China (NSFC) (62173181, 62073171, 61803202), the Natural Science Foundation of Jiangsu Province (BK20200744, BK20180455), Jiangsu Specially-Appointed Professor (RK043STP19001), 1311 Talent Plan of Nanjing University of Posts and Telecommunications, and the Fundamental Research Funds for the Central Universities (30920032203)
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• This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information. First, reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with first-order and second-order players, respectively. In the developed algorithms, the observed disturbance values are included in control signals to eliminate the influence of disturbances, based on which a gradient-like optimization method is implemented for each player. Second, a signum function based distributed algorithm is proposed to attenuate disturbances for games with second-order integrator-type players. To be more specific, a signum function is involved in the proposed seeking strategy to dominate disturbances, based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players’ objective functions. Through Lyapunov stability analysis, it is proven that the players’ actions can approach a small region around the Nash equilibrium by utilizing disturbance observer-based strategies with appropriate control gains. Moreover, exponential (asymptotic) convergence can be achieved when the signum function based control strategy (with an adaptive control gain) is employed. The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform (V-REP) and MATLAB.

• 1 For presentation simplicity, $x_i$ is supposed to be one-dimensional. It is worth mentioning that the presented methods and results are directly applicable to accommodate games with multiple dimensional actions.
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