Tianping Chen

Bo Liu, Wenlian Lu, Licheng Jiao et al.

In this paper, we propose a new self-triggered consensus algorithm in networks of multi-agents. Different from existing works, which are based on the observation of states, here, each agent determines its next update time based on its coupling structure. Both centralized and distributed approaches of the algorithms have been discussed. By transforming the algorithm to a proper discrete-time systems without self delays, we established a new analysis framework to prove the convergence of the algorithm. Then we extended the algorithm to networks with switching topologies, especially stochastically switching topologies. Compared to existing works, our algorithm is easier to understand and implement. It explicitly provides positive lower and upper bounds for the update time interval of each agent based on its coupling structure, which can also be independently adjusted by each agent according to its own situation. Our work reveals that the event/self triggered algorithms are essentially discrete and more suitable to a discrete analysis framework. Numerical simulations are also provided to illustrate the theoretical results.

Tianping Chen

In this short note, we recommend another approach to deal with the topic Consensus of Multi-agents, which was proposed in \cite{Chena}.

Wenlian Lu, Ren Zheng, Tianping Chen

In this paper, we discuss the outer-synchronization of the asymmetrically connected recurrent time-varying neural networks. By both centralized and decentralized discretization data sampling principles, we derive several sufficient conditions based on diverse vector norms that guarantee that any two trajectories from different initial values of the identical neural network system converge together. The lower bounds of the common time intervals between data samples in centralized and decentralized principles are proved to be positive, which guarantees exclusion of Zeno behavior. A numerical example is provided to illustrate the efficiency of the theoretical results.

Ren Zheng, Xinlei Yi, Wenlian Lu et al.

In this paper, we investigate stability of a class of analytic neural networks with the synaptic feedback via event-triggered rules. This model is general and include Hopfield neural network as a special case. These event-trigger rules can efficiently reduces loads of computation and information transmission at synapses of the neurons. The synaptic feedback of each neuron keeps a constant value based on the outputs of the other neurons at its latest triggering time but changes at its next triggering time, which is determined by certain criterion. It is proved that every trajectory of the analytic neural network converges to certain equilibrium under this event-triggered rule for all initial values except a set of zero measure. The main technique of the proof is the Lojasiewicz inequality to prove the finiteness of trajectory length. The realization of this event-triggered rule is verified by the exclusion of Zeno behaviors. Numerical examples are provided to illustrate the efficiency of the theoretical results.

Xiwei Liu, Tianping Chen

In this paper, the fixed-time cluster synchronization problem for complex networks via pinning control is discussed. Fixed-time synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time and the settling time is bounded by a constant for any initial values. To realize the fixed-time cluster synchronization, a simple distributed protocol by pinning control technique is designed, whose validity is rigorously proved, and some sufficient criteria for fixed-time cluster synchronization are also obtained. Especially, when the cluster number is one, the cluster synchronization becomes the complete synchronization problem; when the intrinsic dynamics for each node is missed, the fixed-time cluster synchronization becomes the fixed-time cluster (or complete) consensus problem; when the network has only one node, the coupling term between nodes will disappear, and the synchronization problem becomes the simplest master-slave case, which also includes the stability problem for nonlinear systems like neural networks. All these cases are also discussed. Finally, numerical simulations are presented to demonstrate the correctness of obtained theoretical results.

Xinlei Yi, Wenlian Lu, Tianping Chen

This paper mainly investigates consensus problem with pull-based event-triggered feedback control. For each agent, the diffusion coupling feedbacks are based on the states of its in-neighbors at its latest triggering time and the next triggering time of this agent is determined by its in-neighbors' information as well. The general directed topologies, including irreducible and reducible cases, are investigated. The scenario of distributed continuous monitoring is considered firstly, namely each agent can observe its in-neighbors' continuous states. It is proved that if the network topology has a spanning tree, then the event-triggered coupling strategy can realize consensus for the multi-agent system. Then the results are extended to discontinuous monitoring, i.e., self-triggered control, where each agent computes its next triggering time in advance without having to observe the system's states continuously. The effectiveness of the theoretical results are illustrated by a numerical example finally.