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Applicability and Resilience of a Linear Encoding Scheme for Computing Consensus

Consensus algorithms have a set of network nodes converge asymptotically to a same state which depends on some function of their initial states. At the core of these algorithms is a linear iterative scheme where each node updates its current state based on its previous state and the state of its neighbors in the network. In this paper we review a proposal from control theory which uses linear iterative schemes of asymptotic consensus and observability theory to compute consensus states in a finite number of iterations. This proposal has low communication requirements which makes it attractive to address consensus problems in a limited resource environment such as edge computing. However it assumes static networks contrary to wireless edge computing networks which are often dynamic and prone to attacks. The main purpose of this paper is to assess the network conditions and attack scenarios where this algorithm can still be considered useful in practice to address consensus problems in IoT applications. We introduce some new lower and exact bounds which further improve the communication performance of the algorithm. We also have some technical contributions on how to speed up mitigation of malicious activities and handling network instabilities. Numerical results confirm the communication performance of the algorithm and the existence of scenarios where the system can be considered cost effective resilient to errors injected intentionally or unintentionally.