Distributed Optimization For Multi-Agent Systems With Time Delay

The distributed optimization for multi-agent systems with time delay and first-order is investigated in this paper. The objective of the distributed optimization is to optimize the objective function composed of the sum of local objective functions, which can only be known by its corresponding agents. Firstly, a distributed algorithm for time-delay systems is proposed to solve the optimization problem that each agent depends on its own state and the state between itself and its neighbors. Secondly, Lyapunov-Krasovskii function is used to prove that the states of each agent can be asymptotically the same, and the states are optimal. Finally, an example is given for illustrating the analytical results and a comparison is also gave to illustrate the differences between the algorithm of this paper and other results.