Average Consensus And Containment Control Of Multi-agent Systems With Communication Delays

With the increasing of the networked system, the centralized control strategy has become more and more difficult due to the limitation of network bandwidth and computer processing ability. Distributed control has received more and more attention because of its good modularity, scalability and robustness. Due to the wide applications in military and civilian areas, distributed cooperative control of multi-agent systems has been paid compelling attention. The consensus problem is important and fundamental problem for cooperative control of multi-agent systems, and it is crucial for multi-agents to play its advantages and reflect its performance. In some multi-agent systems, there exist one or even multiple leaders. When there are multiple leaders in the multi-agent systems, the consensus problem becomes a containment control problem. The containment control problem is also an important research topic in cooperative control of multi-agent systems, which has a lot of potential applications in real life. Therefore, this paper not only studies the consensus problem of multi-agent systems, but also considers the containment control problem with multiple leaders. The main contributions of this paper can be summarized as follows:This paper studies the problem of average consensus control for multi-agent systems with linear and Lipschitz nonlinear dynamics under a switching topology. First, a proportional and derivative-like consensus algorithm for linear case with a time delay is designed. By system transformations, such a problem is converted to the stability problem of a switched delay sys-tem. The stability analysis is performed based on a proposed Lyapunov-Krasovskii functional including a triple-integral term and sufficient conditions are obtained to guarantee the average consensus for multi-agent systems under arbitrary switching. Furthermore, extensions to the Lipschitz nonlinear cases are further presented.For the problem that the states of the multi-agent systems with high order general linear dynamic can not be observed, a containment control protocol based on the observer is proposed. The cooperative containment control for multi-agent systems with high-order linear dynamics under a directed graph is studied. First, a follower-based observer based on relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid design-ing the observer for the leaders in the existing literature. In this case, the observers are designed only for followers, instead of all the agents, which reduced the design cost significantly. By in-troducing the matrix transformation, the containment control problem is converted to the stability problem of a autonomous system. By using the Lyapunov function method, sufficient conditions are presented where the controller and observer are designed simultaneously to ensure that the systems achieve containment control, which has superiority over the separate design.The cooperative containment control of multi-agent systems based on follower observers with time delay is studied. In practical applications, due to the existence of such factors as the agent movement, the communication congestion or the limited transmission distance, the influence of time delay on the system is considered. In order to reduce the effect of time delay on the system performance, a distributed control protocol with communication delays is proposed. By a series of transformations, the complex containment control problem is transformed into the stability analysis of time-delay systems. Finally, by constructing a new Lyapunov-Krasovskii function, sufficient conditions on the co-design of the observers and the controllers have been presented.