Time‐varying distributed optimization algorithms with nonuniform gradient gain

In this work, two time‐varying distributed control algorithms are investigated for solving the time‐varying distributed optimization problems of continuous‐time multi‐agent systems with a single‐integrator. One algorithm is developed without an estimator, and the other algorithm is designed with an estimator. It can be proved that under some mild conditions, these two algorithms not only achieve consensus within finite time among all agents, but also minimize the sum of time‐varying convex cost functions. Finally, the effectiveness of the theoretical results is verified through the simulations of distributed optimization controllers designed based on multi‐agent networks.