Consensus of multi-agent systems with Luenberger observers

This paper studies the consensus problem of the multi-agent systems with parallel Luenberger observers. First, the structure of the cooperative system is established, where the output of the built-in Luenberger observer for each agent is used as its local control input and the cooperative control input combining with the cooperative measurement output is utilized as the input of the observers. Based on the structure of the closed-loop system, the consensus problem is then analyzed. In addition, two methods for designing the controller gains are provided. By virtue of the proposed structure, it is pointed out that the design of the controller gains and the observer parameters can be carried out separately. Finally, by resorting to the gradient flow method, an optimization algorithm is proposed to reduce the influence of the environmental noises. The effectiveness of the obtained results is shown through a numerical example.