Dynamics And Control In Impulsive Consensus Of Complex Delayed Networked Multi-agent Systems

The study of cooperative behavior and coordinated control in complex net-worked multi-agent systems has currently become one of the most challenging area of research from various fields such as biology or ecology, physics, applied mathematics, information science, computer science and control theory. This dissertation is mainly concerned with the issues of impulsive consensus prob-lems in complex delayed networked multi-agent systems and the relevant issues from the view of dynamics and control. In details, the fundamental contributions of these works are summarized in the following four aspects:1. Stability theory of impulsive differential equations with any time delays. By utilizing Lyapunov function methods combined with the Razumikhin tech-nique, several criteria on exponential stability are derived analytically, which are substantially the extension and generalization of the corresponding results in re-cent literatures. Compared with some existing works, a distinctive feature of this work is to address exponential stability problems for any time delays, since the restrictive condition that the time delays are less than the length of all the im-pulsive intervals is actually removed here. Moreover, the previous results on Ha-lanay inequality for impulsive delayed dynamical systems are extended. In con-trast to the previous Halanay differential inequality, the primary contribution of this work is to remove the restrictive condition of a priori stability assumption for the corresponding delayed dynamical systems without impulses, so the result can be usually used to stabilize an unstable delayed dynamical system via impulses. Therefore, our work substantially extends the famous Halanay differential in-equality, which will play an important role in stability problems for consensus in delayed networked multi-agent systems, synchronization in complex delayed dynamical networks, control and synchronization in chaotic delayed systems.2. Average consensus problems in directed delayed networked multi-agent systems. By employing the impulsive control theory on delayed dynamical sys- tems, three consensus protocols of the networks with communication delays are proposed. The first is a simple distributed consensus protocol with impulsive effects. And it is shown that a directed delayed networked multi-agent system can achieve average consensus globally exponentially by designing suitable im-pulsive gain and impulsive interval. The second is a distributedδ-consensus protocol in directed networks of dynamic agents having communication delays with stochastic switching communication graphs. The third is a distributed im-pulsive consensus protocol which is valid for any communication delays. Here, the communication delays can be adjusted according to practical demands.3. Impulsive synchronization seeking in general complex delayed dynam-ical networks with nonsymmetrical coupling. Based on the extended Halanay differential inequality, some criteria for global exponential synchronization of the impulsive controlled delayed dynamical networks are derived analytically. The main contributions of the work indicate two aspects:On the one hand, these criteria can provide an effective impulsive control scheme to synchronize an arbi-trary given delayed dynamical networks to a desired synchronization state even if the original given networks may be asynchronous itself. On the other hand, the controlled synchronization state can be selected as any arbitrary weighted average of all the states in the networks for purpose of practical control strategy, which reveals the contributions and influences of various nodes in synchroniza-tion seeking processes of the dynamical networks.4. Impulsive control and synchronization of chaotic delayed systems. By using the impulsive control theory on delayed dynamical systems, some sim-ple yet generic criteria to guarantee impulsive stabilization and synchronization for a class of chaotic delayed systems are analytically derived. Subsequently, the generalized Halanay differential inequality in vector form may be applied to chaos-based secure communication systems with transmission delay, where a driving system and a response system are employed. Finally, a model of re-current neural networks with time-varying delays in the presence of impulsive connectivity among the neurons is addressed. Moreover, numerical simulations are worked out to further illustrate our theoretical results.