Joshua Ogbebor

This paper examines the roles of the matrix weight elements in matrix-weighted consensus. The consensus algorithms dictate that all agents reach consensus when the weighted graph is connected. However, it is not always the case for matrix weighted graphs. The conditions leading to different types of consensus have been extensively analysed based on the properties of matrix-weighted Laplacians and graph theoretic methods. However, in practice, there is concern on how to pick matrix-weights to achieve some desired consensus, or how the change of elements in matrix weights affects the consensus algorithm. By selecting the elements in the matrix weights, different clusters may be possible. In this paper, we map the roles of the elements of the matrix weights in the systems consensus algorithm. We explore the choice of matrix weights to achieve different types of consensus and clustering. Our results are demonstrated on a network of three agents where each agent has three states.

Wireless Sensor Networks (WSNs) are broadly applied for various applications in tracking and surveillance due to their ease of use and other distinctive characteristics compelled by real-time cooperation among the sensor nodes. In WSNs, security is becoming a critical issue, as the techniques for malicious node detection adopt a one-time, centralized decision-making approach. With this paradigm, errors are difficult to avoid, and reproducibility and traceability are challenging. Hence, malicious node discovery technologies in conventional WSNs cannot assure traceability and fairness of the detection method. Herein, this paper discusses an in-depth survey of a blockchain-based approach for malicious node detection, an exhaustive examination of the integration of blockchain techniques with WSNs (BWSN), and insights into this novel concept. This survey discusses the architecture, sector-wise applications, and uses of BWSN. Moreover, this survey describes malicious node detection based on BWSN in two parts: 1) the BWSN architecture for detecting the malicious nodes and 2) the smart contract aspects in malicious node detection. Next, this survey explains the contributions of blockchain for WSN data management, which involves online information aggregation and may include auditing, event logs, and storage for information analysis and offline query processing. This survey first presents the conventional WSN solutions then the blockchain-based WSN solutions for data management. Additionally, this survey discusses the contributions of blockchain for WSN security management. It first examines the centralized WSN models for security problems, followed by a discussion of the blockchain-based WSN solutions for security management, such as offering access control, preserving information integrity, guaranteeing privacy, and ensuring WSNs’ node longevity.

This paper extends the concept of weighted graphs to matrix weighted graphs. The consensus algorithms dictate that all agents reach consensus when the weighted graph is connected. However, it is not always the case for matrix weighted graphs. The conditions leading to different types of consensus have been extensively analysed based on the properties of matrix-weighted Laplacians and graph theoretic methods. However, in practice, there is concern on how to pick matrix-weights to achieve some desired consensus, or how the change of elements in matrix weights affects the consensus algorithm. By selecting the elements in the matrix weights, different clusters may be possible. In this paper, we map the roles of the elements of the matrix weights in the systems consensus algorithm. We explore the choice of matrix weights to achieve different types of consensus and clustering. Our results are demonstrated on a network of three agents where each agent has three states.