An adaptive finite-time neurodynamic approach to distributed consensus-based optimization problem

In this paper, a novel distributed adaptive neurodynamic approach (DANA) based on proportional integral technique is proposed to solve distributed optimization problem on multi-agent systems. The goal is that all agents reach consensus in finite time and converge to the optimal solution of the global objective function in fixed time. In the proposed approach, the proportional technique drives all agents to reach consensus, and the integral technique is used to offset the influence of the gradient term of the objective function. On the other hand, in order to avoid the prior estimation of gain parameter and the global gradient information, as the main contribution of this paper, the adaptive idea is considered into proportional integral technique. The results show that the adaptive integral technique can automatically adjust the gain according to the maximum consensus error between agents, so as to ensure that agents can achieve consensus in finite time. Then the theoretical results are applied to voltage distribution and logistic regression. Numerical simulation verifies the effectiveness of DANA.