Synchronization Control for Large-Scale Network Systems

With the rapid development of intelligent instrument and digital measurement, modern control systems tend to be controlled by digital signal processing approaches, i.e. the control input signals are kept constant via a ZOH during the sampling instants and are only allowed to change at the discrete time instants. Thus, sampled-data control problem has been a hot research topic and numerical essential approaches have been derived in the literature, which include three main models: discrete-time model (Zhang et al., IEEE Control Syst Mag, 21:84–99, 2001, [1]), impulsive model (Hu et al., IEEE Trans Syst Man Cybern Part B Cybern, 33(1):149–155, [2]) and input delay model (Fridman et al., Syst Control Lett, 54(3):271–282, [3]).

Sampled-data systems contain continuous-time plants under discrete-time control updates [1‐9]. Although using periodic sampling may be adequate for some cases [10, 11], it is usually required to use the nonuniform sampling pattern in resource constrained scenarios to further reduce the energy, computation and communication costs. Several approaches have been proposed for the analysis of aperiodic sampled-data systems. In [12], the stability condition is obtained in a convex polytope and is considered as time-varying uncertainties. In [13], the ‘input-delay approach’ is used to reformulate the original sampled-data system into time-delay system. In [14], the discrete-time Lyapunov theorem is utilized to analyse the continuous-time systems and relax the certain conditions required in the input-delay approach. In [15], method based on impulsive system is investigated by using clock-dependent Lyapunov functional, and this method can characterize the robust stability of sampled-data system in both the certain and uncertain cases.

Much attention has been drawn to the study of LSNSs over the last decade, because LSNSs are successfully applicable to describe a variety of real world systems including Internet networks, biological networks, epidemic spreading networks, collaborative networks, and social networks (Liu et al., IEEE Trans Neural Netw 20:1102–1116, 2009, [3]; Wang et al., IEEE Trans Neural Netw 21:11–25, 2010, [6]).

The distributed synchronization of LSNSs is a significant topic and has attracted a lot of attention (Ren and Beard, Distributed consensus in multi-vehicle cooperative control: theory and applications. Springer, Berlin, [1], Su et al., IEEE Trans Autom Control 58(5):1275–1279, [2], Yu et al., Automatica 49(7):2107–2115, [3], Yu et al., IEEE Trans Ind Inf 9(4):2137–2146, [4], Meng et al., Automatica 70:173–178, [5]. In the leader-follower framework, the followers aim to track the leader’s motion, which is independent of all followers and is not available to all of them (Ni and Cheng, Syst Control Lett 59(3):209–217, [6], [1].

Recently, the synchronization problem of LSNSs has attracted considerable attention in systems and control community, due to its application to a wide range of problems, including sensor networks, rendezvous, formation control and flocking control [1‐12]. The agents exchange information through a communication graph, which is a time-varying graph [13‐16] or a time-invariant graph [17‐20]. The dynamics of individual agents in the network can be identical.

Due to the ability to describe a wide range of complicated systems in real applications, the LSNSs have spurred great interests in various disciplines, such as physics, social sciences and engineering.

LSNSs has widespread applications in various fields, such as distributed filtering of sensor networks, surveillance systems, intelligent transportation management systems, cooperative control of unmanned air vehicles, data fusion of multi-sensor networks [1‐9]. Since agents in LSNSs are coupled with the topological evolution, the analyses on the dynamical behaviors of LSNSs are more challenging than the single system. Synchronization for some variables of the LSNSs is a kind of typical collective behaviors and has extensively investigated recently, which means that the variables of LSNSs asymptotically converge to the same trajectories. However, only local information is available for each agent, i.e., each agent cannot obtain all the information about other agents.

The studies of LSNSs have received tremendous attention over decades due to its widespread applications in various fields, such as sensor networks, intelligent transportation management systems, UAVs, fuel cell systems, etc.

The synchronization problem of LSNSs has attracted considerable attention due to its widely applications, see for example, [1‐9], and the references therein. In the leader-follower framework, the leader’s motion is independent of all the followers and followed by them [10]. The dynamics of the individual followers can be non-identical [11, 12] or identical [13]. For the case of non-identical followers, the output regulation theory is a valuable method to handle the synchronization problem [14, 15].