Synchronization analysis and control for complex dynamical networks

Abstract

Complex dynamical networks (CDNs) are ubiquitous in our real world, ranging from biological, social, to man-made networks. Many interesting phenomena can be observed in CDNs. Among them, synchronization has been a hot research topic in recent years due to its potential applications. Synchronization emerges from the interconnections of CDNs, but the final synchronous state is difficult to predict. However, for many social, biological and physical dynamical networks, there is a common requirement to regulate the final behavior of large ensembles of interacting units. It is desirable to design controllers to force the unpredicted final synchronous state to certain required objective states. Hence, there is a great demand to study synchronization behavior and the control of CDNs. There are some common phenomena in many evolutionary networks including communication delays, switching topology, signal noise and impulsive effects. This thesis presents our research and developments on the corresponding concerned issues of synchronization analysis and the control problem of CDNs. Three classes of dynamical networks with delay-coupling, switched structures and impulsive signals are respectively presented. We are mainly concerned with the following problems: (a) synchronization criteria of different kinds of dynamical networks; (b) the stabilization of dynamical networks via different kinds of controllers; (c)the stabilization of dynamical networks under performance constraint; (d) and impulsive dynamical networks. For problem (a), synchronization criteria are derived to verify whether synchronization of state-coupled and delay-coupled dynamical networks can be achieved. The synchronizability of dynamical networks is also discussed. The constraint that the coupling configuration matrix is symmetric and irreducible, which is frequently used in other literature, is removed. For problem (b), adaptive controllers and pinning state-feedback control are, respectively, designed for the stabilization of various kinds of dynamical networks. The minimum number of pinning controllers is used to force the CDNs into certain objective state. For problem (c), we investigate the dynamical network with both intrinsic disturbance of single node and communication noise over the network connections. Hinfinity controller is used for the exponential stabilization of dynamical network, and the prescribed performance constraint is simultaneously satisfied. For problem (d), there are two kinds of opposite impulses: synchronizing impulse and desynchronizing impulse. We derive unified criteria to study the synchronization of CDNs under the effects of synchronizing or desynchronizing impulses. Single impulsive controller is designed to stabilize impulsive dynamical networks. The main contributions of this thesis are listed as follows: (i) our results are available for large-scale dynamical networks; (ii) diverse delays are verified to be quite robust against the consensus of multi-agent systems; (iii) single impulsive controller is designed for the stabilization of CDNs; (iv) the minimum number of pinning controllers is obtained; (v) and unified criteria are proposed for the synchronization of CDNs with synchronizing or desynchronizing impulses.