Extended state observer based resource allocation method for second-order multi-agent systems with time-varying disturbances

This paper investigates the resource allocation problems for a class of second-order multi-agent systems with time-varying disturbances, where each agent only knows its own state information, its local cost function, and the state information of its neighbors. The aim is to design a distributed resource allocation algorithm such that the agents can make appropriate decisions to minimize the global cost function under the constraint of network resources and time-varying disturbances, where the global cost function is the sum of all local cost functions. In order to achieve the purpose of disturbance rejection, the paper proposes a new distributed resource allocation algorithm based on active disturbance rejection control, which is composed of disturbance compensation term, state feedback term and local gradient descent term. Moreover, based on the convex analysis and Lyapunov stability analysis methods, we prove that when the time tends to infinity, the decisions of the agents converge to any small neighborhood of the optimal resource allocation under the time-varying disturbances. Finally, the simulation results show the effectiveness of the proposed optimization algorithm.