Exponential convergence of distributed optimization for heterogeneous linear multi-agent systems over unbalanced digraphs

Abstract

In this work we study a distributed optimal output consensus problem for heterogeneous linear multi-agent systems over unbalanced directed networks where the agents aim to reach consensus with the purpose of minimizing the sum of private smooth costs. Based on output feedback, a distributed continuous time control law is proposed by using the proportional–integral (PI) control technique. Under the assumption that the global cost function satisfies the restricted secant inequality condition, the designed controller can achieve convergence exponentially in an unbalanced and strongly connected network. Furthermore, to remove the requirement of continuous communications, a sampling-based event-triggered algorithm with a lower bound of the communication interval is provided, which also converges exponentially. Two simulation examples are given to verify the proposed control algorithms.