Distributed Optimization of Second-Order nonlinear Multi-Agent Systems Subject to Communication Delays

In this paper, the distributed optimization problem of continuous-time second-order nonlinear multi-agent systems with communication delays under undirected graphs is studied. First, we show that the equilibrium point of the multi-agent systems with time delays is corresponding to the optimal solution of the problem. Next, based on gradient descent, we propose a distributed optimization algorithm. Besides, we analyze the global convergence of the algorithm by constructing a suitable Lyapunov function and linear matrix inequality. Finally, an example is presented to illustrate the effectiveness of our result.

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