Abstract
In this paper, we address the resilient group consensus of multi-agent networks in the presence of structured and unstructured Byzantine faults. In the case of structured Byzantine faults that feed different but structured values to the network, it is shown that non-faulty nodes can achieve group consensus without using any fault tolerant algorithm. Necessary and sufficient conditions on the network are derived so that the conventional consensus algorithm leads to group consensus values in the range determined by the initial values of the non-faulty nodes. In the presence of unstructured Byzantine faults, two fault tolerant algorithms are proposed to overcome the highly disruptive behaviour. Subsequently, convergence analysis of these algorithms is carried out by exploiting the robustness properties of the network. Finally, theoretical results are illustrated with several simulation examples.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 Throughout the paper, the term agent is interchangeably referred to as node.
2 A spanning tree exists in a digraph if there exists a directed tree formed by directed graph edges that connect all the nodes of the graph (Godsil & Royle, Citation2013).
3 Given two graphs and , is said to be a subgraph of G if and hold for .
4 The notation is used to model faulty behaviour, whereas refers to the non-faulty behaviour, i.e. is the state value of the faulty node j that is sent to node i and is the state value of the non-faulty node i.
5 Pseudo-code of the L-MSR algorithm is given in Algorithm 1.
6 Minimum in-degree of a graph G, denoted by , is the minimum number of incoming edges for all vertices of the graph G (LeBlanc et al., Citation2013).