Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

On Hybrid Adaptive and Pinning Consensus for Multiagent Networks

The consensus problems for both continuous-time and discrete-time multiagent networks are deeply investigated by adopting hybrid adaptive and pinning control laws, respectively. Particularly, the topology of the networks needs to neither be symmetric nor contain a directed spanning tree and some useful criteria are addressed analytically. Simultaneously, a comprehensive pinning scheme is proposed as well which shows that the nodes with zero in-degree need to be pinned primarily in order to guarantee the system to achieve consensus, and then the nodes whose out-degrees are bigger than their in-degrees can give priority to be pinned compared to other nodes for improving the convergence rate of the system, whereas it is also interesting to find out that the regular rule does not always hold, that is, the more nodes are selected to be pinned, the faster the system will converge. Finally, the validity of our theoretical findings is verified by several numerical examples.

Control of Multiagent Systems: A Stochastic Pinning Viewpoint

A stochastic pinning approach for multiagent systems is developed, which guarantees such systems being almost surely stable. It is seen that the pinning is closely related to being a Bernoulli variable. It has been proved for the first time that a series of systems can be stabilized by a Brownian noise perturbation in terms of a pinning scheme. A new terminology named “stochastic pinning control” is introduced to describe the given pinning algorithm. Additionally, two general cases that the expectation of the Bernoulli variable with bounded uncertainty or being unknown are studied. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed methods.

Pinning Synchronization of One-Sided Lipschitz Complex Networks

This paper studies the pinning synchronization in complex networks with node dynamics satisfying the one-sided Lipschitz condition which is less conservative than the well-known Lipschitz condition. Based on M-matrix theory and Lyapunov functional method, some simple pinning conditions are derived for one-sided Lipschitz complex networks with full-state and partial-state coupling, respectively. A selective pinning scheme is further provided to address the selection of pinned nodes and the design of pinning feedback gains for one-sided Lipschitz complex networks with general topologies. Numerical results are given to illustrate the effectiveness of the theoretical analysis.

Synchronization of Neuronal Networks via Control Rank Pinning Scheme

Recent studies have proposed the controlling regions in the corticocortical network of cats' brain at different scales. Here we study pinning control using a simple model of coupled oscillators assigned to cortical areas in the corticocortical network of cats' brain. We analyze control rank (CR) values of areas in the cortical network. It is found that most of the hubs have bigger CR values than other nodes in the same functional community. Moreover, we analyze the synchrony state of the functional communities in the cortical network, revealing that a community with a larger percentage of pinned nodes inside will be conducive to synchronization.