Distributed optimal coordination of multi-agent systems with coupled objective functions: A fixed-time estimation-based approach

Abstract

This paper explores a class of distributed optimal coordination problems with coupled objectives, incorporating features of distributed optimization and non-cooperative game. In this context, the local objective functions of agents depend on their own decisions as well as the decisions made by other agents. The objective of the agents is to achieve optimal coordination by minimizing the team objective function, which represents the average of all agents’ local objective functions. The main challenge lies in obtaining the partial derivatives of the team objective function, which are aggregations of all local objective functions’ partial derivatives and cannot be directly obtained by the agents. To tackle this problem, distributed optimal coordination control laws based on fixed-time estimation are developed. These control laws utilize distributed fixed-time estimators that enable agents to estimate the team decision and partial derivatives of the team objective function within a fixed time. The proposed distributed optimal coordination control laws guarantee the exponential convergence of the agents to the optimal states when the constraint sets are independent. Under the condition of a common constraint set, the proposed laws further ensure fixed-time optimal coordination. A numerical example involving coordinated dynamic positioning of a multi-agent system is presented to demonstrate the effectiveness of the proposed algorithms.