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Distributed Nash equilibrium seeking for constrained aggregative games subject to disturbances with unknown bounds
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DOI：10.1016/j.automatica.2026.113029.png)
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Abstract
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The distributed Nash equilibrium (DNE) seeking problem for aggregative games has been extensively studied for unconstrained case over all types of communication networks and for various types of constrained games over static and connected communication networks. In this paper, we first investigate the DNE seeking problem for constrained aggregative games over jointly connected and weight-balanced switching networks, which can be directed and disconnected at every time instant. By integrating the projected gradient technique and the dynamic average consensus algorithm, we convert our problem to a stability analysis problem of a well-defined time-varying nonlinear system. By constructing a time varying Lyapunov’s function candidate for this time-varying nonlinear system, we conduct a detailed Lyapunov analysis to conclude the exponential stability of this system and hence solve our problem. Then we further study the DNE seeking problem for constrained aggregative games over jointly connected and weight-balanced switching networks for the case where the action variables are governed by high-order integrator systems subject to unknown bounded disturbances. By further incorporating the adaptive control technique into the control law of the first case, we manage to solve this more complicated case. The effectiveness of our approach is validated by an energy consumption game and a formation coordination example.
Keywords:
Distributed Nash equilibrium
Aggregative games
Constrained games
Switching networks
Adaptive control
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