Cyber-physical Defense for Heterogeneous Multi-agent Systems Against Exponentially Unbounded Attacks on Signed Digraphs

TL;DR

This work addresses the containment of outputs in heterogeneous multi-agent systems under exponentially unbounded false data injection attacks on both cyber and observer layers. It introduces a fully distributed bilayer defense comprising a privacy-preserving observer layer and a cyber-physical layer controller, with adaptive masking and attack-resilient dynamics validated by Lyapunov-based $UUB$ guarantees. The main contributions include a privacy-preserving mechanism for leader data, a fully distributed attack-resilient observer, and a compensating controller that ensures containment within the leaders’ convex hull despite EU-FDI. Numerical and microgrid experiments demonstrate enhanced resilience and privacy, indicating practical implications for secure, cooperative CPS deployments like UAV swarms and microgrids.

Abstract

Cyber-physical systems (CPSs) are subjected to attacks on both cyber and physical spaces. In reality, the attackers could launch exponentially unbounded false data injection (EU-FDI) attacks, which are more destructive and could lead to the system's collapse or instability. Existing literature generally addresses bounded attack signals and/or bounded-first-order-derivative attack signals, which exposes the CPSs to significant threats. In contrast, this paper proposes a fully-distributed attack-resilient bi-layer defense framework to address the bipartite output containment problem for heterogeneous multi-agent systems on signed digraphs, in the presence of EU-FDI attacks on both cyber-physical layer (CPL) and observer layer (OL). First, we design attack-resilient dynamic compensators that utilize data communicated on the OL to estimate the convex combinations of the states and negative states of the leaders. The attack-resilient compensators address the EU-FDI attacks on the OL and guarantee the uniformly ultimately bounded (UUB) estimation of the leaders' states. Then, by using the compensators' states, fully-distributed attack-resilient controllers are designed on the CPL to further address the EU-FDI attacks on the actuators. Rigorous mathematical proof based on Lyapunov stability analysis is provided, establishing the theoretical soundness of the proposed bi-layer resilient defense framework, by preserving the UUB consensus and stability against EU-FDI attacks on both CPL and OL. Finally, a comparative case study for heterogeneous multi-agent systems validate the enhanced resilience of the proposed defense strategies.

Figures (11)

• Figure 1: Cyber-physical layer and observer layer.
• Figure 2: The overall closed-loop cyber-physical dynamical system.
• Figure 3: Communication topology.
• Figure 4: Bipartite output containment errors $e^s_{y_i}$ using the standard control protocols: $e^s_{y_i}(1)$ is the $x$ coordinate of $e^s_{y_i}$, $e^s_{y_i}(2)$ is the $y$ coordinate of $e^s_{y_i}$.
• Figure 5: Bipartite output containment errors $e^s_{y_i}$ using the proposed resilient control protocols: $e^s_{y_i}(1)$ is the $x$ coordinate of $e^s_{y_i}$, $e^s_{y_i}(2)$ is the $y$ coordinate of $e^s_{y_i}$.

Theorems & Definitions (21)

• Remark 1
• Definition 1: Structurally balancedvalcher2014consensus
• Definition 2: Convex hullrockafellar2015convex
• Definition 3: Distance
• Definition 4: UUBkhalil2002nonlinear
• Remark 2
• Lemma 1: valcher2014consensus
• Lemma 2: zuo2018bipartite
• Lemma 3: huang2004nonlinear
• Definition 5: altafini2019dynamical