# Redundancy-Reduction-Based Hierarchical Design in Synchronization of Multi-Agent Systems
###### Abstract  
In this paper, a layered, undirected-network-structure, optimization approach is proposed to reduce the redundancy in multi-agent information synchronization and improve the computing rate. Based on the traversing binary tree and aperiodic sampling of the complex delayed networks theory, we proposed a network-partitioning method for pinning dynamic networks, with a more simplified, analyzable structure, and all of the traversed nodes are mathematically asymptotically synchronized at the same time. Moreover, a systematic implementable approach is proposed for application. The approach could be separated into two main  
on the control-oriented investigations, and simultaneously, neural networks have faced their boom era, a huge amount of computational cost pressure makes the last two directions mentioned above especially important. The mathematical analysis of synchronization is strengthened for reducing conversation [10; 11], optimizing calculation [12], and maximizing available resources [13; 14] and limited application scenarios. With the deepening of research, it is becoming increasingly difficult to rely on mathematical algorithms to improve efficiency. In view of this, researchers gradually turned to other approaches. By measuring the similarity between different data sources, and classified with multiple clusters, the pre-processing by cluster analysis can analyze various methods for different types of data, which greatly simplifies the data analysis process and is one of the most visible and explainable concepts in computer science. By applying the clustering analysis method to the large-scale complex dynamic network structure decomposition, the nodes with large correlations of properties are classified so that large-scale networks can be simplified and analyzed for a limited number of small-scale networks; thus, the network model could be simplified and the number of calculations could be reduced. The main structure of the network is also made clearer by the extraction of the main nodes. [PERSON] et al. [15] created a framework of an analysis method for network dynamics to show the connection between cluster formation and network symmetries. This finding provides the fundamental contributions to the analysis of the clustering of the dynamic network. Then, some early related applications have emerged. In [16], based on eigenvalue decomposition, the authors proposed a centralized adaptive intermittent control approach to make cluster synchronization. By applying the adaptive approach, [PERSON] et al. [17] proposed sufficient conditions to guarantee global cluster synchronization for linearly coupled networks, which could be applied in neural calculation to save computations. Oriented from the pinning control strategy, the authors [18] also found a new way to drive a general network to a selected cluster synchronization pattern. Considering an array of hybrid coupled neural networks with delay, based on Lyapunov stability theory and linear matrix inequality(LMI) method, [PERSON] and [PERSON] [19] proposed several sufficient conditions for cluster synchronization. It should be pointed out that compared with existing work, the coupling configuration matrix and inner coupling matrix have greater applicability. Additionally, relative works could also be seen in [20; 21; 22; 23; 24; 25]. It is worth pointing out that there is some good work being done in some emerging and intersecting areas, such as AI-driven packet forwarding [26] and the services of the customized industrial Internet of things [27]. Considering that the algorithms mentioned above have made great progress in mathematics and application, the algorithms may be more complex, and many solutions are only suitable for some specific scenarios, which has led to the development of a wide range of applications and better operability.