Resilient Consensus of Second-Order Agent Networks: Asynchronous Update Rules with Delays (1701.03430v2)

Abstract: We study the problem of resilient consensus of sampled-data multi-agent networks with double-integrator dynamics. The term resilient points to algorithms considering the presence of attacks by faulty/malicious agents in the network. Each normal agent updates its state based on a predetermined control law using its neighbors' information which may be delayed while misbehaving agents make updates arbitrarily and might threaten the consensus within the network. Assuming that the maximum number of malicious agents in the system is known, we focus on algorithms where each normal agent ignores large and small position values among its neighbors to avoid being influenced by malicious agents. The malicious agents are assumed to be omniscient in that they know the updating times and delays and can collude with each other. We deal with both synchronous and partially asynchronous cases with delayed information and derive topological conditions in terms of graph robustness.

• The paper studies resilient consensus in second-order agent networks with asynchronous updates and delays, using adaptive mean subsequence reduced (MSR) algorithms to counter malicious agents.
• For synchronous networks, the Double-Integrator Position-Based MSR (DP-MSR) algorithm ensures resilient consensus if the graph is (f+1,f+1)-robust, where f is the maximum number of malicious agents.
• Extending to asynchronous networks with delays, the DP-MSR algorithm requires a stricter (2f+1)-robust graph property for resilient consensus using the most recent neighbor information.

Resilient Consensus of Second-Order Agent Networks: Asynchronous Update Rules with Delays

The paper undertakes a paper of resilient consensus algorithms in multi-agent networks characterized by second-order dynamics, specifically focusing on scenarios where nodes face asynchronous update rules and time delays. Authored by Seyed Mehran Dibaji and Hideaki Ishii, the research explores adaptive strategies for network management amidst adversarial disruptions caused by malicious agents. Supported by theoretical rigor, the authors present a systematic approach to maintaining network consensus.

Summary of Main Contributions

The paper is premised on networks where each agent adheres to double-integrator dynamics, presenting a common framework for mobile robots and autonomous vehicles. The research assumes scenarios with potential malicious agents capable of arbitrary behavior, thereby requiring agents to engage in resilient consensus algorithms. Specifically, the paper presents an adaptation of mean subsequence reduced (MSR) algorithms to withstand adversarial conditions by omitting extreme position values from computation.

1. Synchronous Networks with MSR Algorithms:
   • The paper introduces the Double-Integrator Position-Based MSR (DP-MSR) algorithm for synchronous update environments. This algorithm proposes that each normal agent should disregard extreme positive and negative position values from neighboring agents—effectively mitigating the impact of malicious agents.
   • Results demonstrate that resilient consensus is achievable in synchronous networks if the graph meets $(f+1,f+1)$-robustness, where $f$ is the maximum number of malicious agents.
2. Partial Asynchrony and Delay Resilience:
   • Addressing realistic conditions of asynchronous updates and delays, the paper extends the DP-MSR algorithm to accommodate these constraints. Here, normal agents use the most recent neighbor information, adopting a conservative approach to mitigating delays through robust graph theory.
   • The associated requisite graph property shifts to $(2f+1)$-robustness, reflecting a heightened need for connectivity to manage the complexities introduced by asynchronous operations and delays.

Theoretical Implications

The introduction of graph robustness criteria within the context of MSR algorithms for second-order systems sets a novel foundation for analyzing consensus problems in dynamic networks. The establishment of necessary and sufficient conditions in terms of $(f+1,f+1)$ and $(2f+1)$ graph robustness provides a quantifiable measure, linking topology directly to system stability and resilience.

Practical Significance

In practical terms, the research delivers insights critical to designing resilient networked systems, especially where individual nodes may experience adversarial attacks. Autonomous vehicles and robotic formations—a core application focus—stand to benefit from the DP-MSR algorithm, ensuring functional integrity even when a subset of nodes become compromised. The adaptation to asynchronous systems further advances applicability, accommodating real-world communication delays and asynchronous updates common in wireless systems.

Prospects for Future Research

While the paper effectively addresses double-integrator dynamics within granted delay bounds, future research can explore further relaxation of these constraints, examining scenarios where delay bounds are unknown or dynamically varying. Additionally, extending the robustness conditions to even more general network topologies could pave the way for wider adoption in varied engineering contexts.

In conclusion, this paper by Dibaji and Ishii presents a significant contribution to the field of networked control systems, particularly in enhancing the security and reliability of multi-agent systems in the face of adversarial conditions. The findings are pivotal for researchers and practitioners formulating strategies to bolster resiliency in distributed networks across diverse applications.