Resilient distributed algorithms for solving linear algebraic equations in faulty networks

Various methods have been developed to solve linear algebraic equations distributively over multi-agent networks. Most studies consider that all agents are trustworthy and utilize all the received data from their neighbors throughout the process. Nevertheless, cooperation between non-faulty agents is disrupted if faulty agents intrude into the network. This thesis aims to develop algorithms to detect all faulty agents in the network without prior knowledge of the number of faulty agents. We study four fault models: random-state, fixed-state, single-faced, and double-faced and propose fault detection procedures according to the characteristics of these fault models. First, we introduce a method in which each agent can determine its neighbors' system of equations if it receives sufficient solution estimations from neighboring agents. By utilizing this method, we propose a synchronous discrete-time distributed detection algorithm for the perfectly synchronized agents in terms of their event times. On the other hand, the event time sequences of different agents are not always assumed to be synchronized. Therefore, we also propose an asynchronous discrete-time distributed fault detection algorithm to analyze the effect of the asynchronous event times of agents. Also, we discuss the applicability of our detection algorithm in continuous-time systems. Moreover, complexity analyses for the proposed algorithms are carried out. Theoretical results are also illustrated by numerical examples.