Distributed Adaptive Generalized Nash Equilibrium Algorithm for Aggregative Games
With the development of cyber-physical system technology,the distributed cooperative optimization problem for multi-agent systems has been widely studied.This study focuses on the distributed constrained aggreg-ative game for multi-agent systems,where the local cost function is subject to the global aggregative and global equality constraints.Firstly,a Nash equilibrium seeking algorithm based on estimation gradient descent is designed for the first-order integrator-based multi-agent systems.To this end,an adaptive estimation scheme is designed us-ing the average consensus method of multi-agent systems to realize the distributed estimation of global aggregative function.Based on this,the estimation gradient function is calculated.Secondly,the above algorithm is extended to the state-accessible and state-inaccessible general heterogeneous linear multi-agent systems using the state and out-put feedback control scheme,respectively.Finally,the convergence proof is provided using the LaSalle's invariance principle and several simulation examples are provided for illustrating the effectiveness of our proposed algorithms.
Aggregative gameadaptiveproportional-integralgradient trackinggeneral linear multi-agent system
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