Distributed Accelerated NE Seeking Algorithm With Improved Transient Performance: A Hybrid Approach

This article studies a distributed Nash equilibrium (NE) seeking problem for multiple agents of aggregative games. A novel distributed algorithm is presented to assure both fast convergence and nonovershoot performance by the combination of an accelerated method and a gradient-based NE seeking algorithm. To be specific, an accelerated method (i.e., the heavy-ball method or Nesterov’s accelerated method) is introduced in the designed algorithm for the fast convergence of agents’ strategies to the NE. Moreover, a suitable switching mechanism is proposed to improve the transient performance by switching the distributed algorithm based on the accelerated method to the gradient-based algorithm. As a result, the presented distributed algorithm is modeled by a hybrid dynamical system (HDS). The semi-globally practical convergence is established by analyzing the stability of a parameterized HDS. An example of distributed energy resources is taken to verify the presented algorithm.