Resilient Output Containment of Heterogeneous Multi-Agent Systems Against Byzantine Attacks

This study focuses on addressing distributed Byzantine-resilient output containment issues for heterogeneous continuous-time multi-agent systems. Inspired by the digital twin technology which creates a virtual replica of a physical object or system, a virtual layer named twin layer is introduced in this work, which is parallel to the conventional cyber-physical layer. The twin layer is more secure than the cyber-physical layer, which generates the secure reference trajectory of each agent via real-time data processing and simulation. Moreover, it decouples the resilient output containment against Byzantine attacks (BA) into two defense sub-schemes: One on the twin layer against Byzantine edge attacks (sending wrong and different messages to neighbors) and the other on the cyber-physical layer against Byzantine node attacks (falsifying input signals). On the twin layer, we develop a topology-assignable distributed resilient estimator by utilizing a novel secure centroid approach, which enhances the resilience of the twin layer by adding a minimal fraction of trusted edges. It is proved that achieving strong $[({n+1})f+1]$-robustness towards the leader set is adequate for ensuring the resilience of the twin layer. On the cyber-physical layer, we design a decentralized adaptive controller against Byzantine node attacks and can also handle potential inter-layered controller faults. This novel adaptive controller has the merit of converging exponentially at an adjustable rate, whose error bound can be explicitly stated. Consequently, we manage to address the resilient containment problem against BAs, in which the agents subject to Byzantine node attacks can also achieve output containment instead of just the normal agents. The simulation examples confirm the efficacy of this newly developed hierarchical protocol, where both normal and Byzantine followers converge within the dynamic convex hull formed by the normal leaders.