Leader-Follower Formation Control of Multi-Agent Systems: A Hybrid Approach.

In recent years, significant attention has been focused on the control of multi-agent systems due to their potential to perform complex tasks that single-agent systems cannot achieve. These tasks include network consensus, formation control, flocking, leader synchronization, space rendezvous, and cooperative output regulation, with applications in diverse fields such as mobile robotics, sensor networks, autonomous vehicles, and electrical power systems. This doctoral thesis proposes a novel approach to address the challenges of designing formation control for leader-follower multi-agent systems under intermittent communications. A linear hybrid distributed observer is proposed to estimate the leader’s reference signal for each follower, ensuring accurate estimation despite intermittent communication among agents. The proposed approach demonstrates global exponential stability in the reference estimation error for each agent. Furthermore, this thesis addresses the cooperative output regulation problem for uncertain linear multi-agent systems under asynchronous intermittent measurements. A hybrid distributed observer and control law are developed to handle the communication constraints between agents, with the system’s stability and regulation conditions guaranteed by a solution to a set of linear matrix inequalities. The controller design is based on a leader-follower scheme with a virtual leader, given by an exosystem, and a set of followers, modeled as heterogeneous linear systems with uncertainties. The communication structure is proposed under a directed graph, which only needs to be available at least once between two-time bounds, solving the frequent problems of switching topologies and Zeno-like behaviors. The stability and regulation conditions of the multi-agent system are proved and guaranteed under the existence of a solution to a finite set of linear matrix inequalities. The effectiveness of the proposed approach is demonstrated by numerical simulations, and compared with existing results in the literature. An example of multi-agent systems with heterogeneous followers is also applied to demonstrate the performance of the proposal. Finally, this work tackles the cooperative output regulation of switched linear multi-agent systems with asynchronous intermittent transmissions. A hybrid distributed control law is developed for leader synchronization in scenarios with heterogeneous agent dynamics, where the switching signals between subsystems are modeled within a hybrid framework. The stability and regulation conditions of the multi-agent system are demonstrated, and the effectiveness of the proposed methodologies is proved through numerical simulations. The proposed contributions ensure robust performance and significantly enhance the overall stability and synchronization of multi-agent systems under asynchronous intermittent measurements, marking a substantial advancement in the field of formation control and cooperative output regulation.