Engineering consensus in static networks with unknown disruptors

Abstract: Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems are inherently vulnerable to disruption. To develop a resilient consensus approach, inspiration is taken from the study of social systems and their dynamics; specifically, the Deffuant Model. A dynamic algorithm is presented enabling efficient consensus to be reached with an unknown number of disruptors present within a multi-agent system. By inverting typical social tolerance, agents filter out extremist non-standard opinions that would drive them away from consensus. This approach allows distributed systems to deal with unknown disruptions, without knowledge of the network topology or the numbers and behaviours of the disruptors. A disruptor-agnostic algorithm is particularly suitable to real-world applications where this information is typically unknown. Faster and tighter convergence can be achieved across a range of scenarios with the social dynamics inspired algorithm, compared with standard Mean-Subsequence-Reduced-type methods.

• The paper introduces the novel ODDI-C algorithm that leverages social dynamics to achieve consensus without predefined disruptor information.
• It employs dynamic tolerance and median-based z-scores to filter extreme opinions, resulting in faster convergence compared to traditional methods.
• Experimental validation demonstrates ODDI-C’s superior resilience in varied network conditions, maintaining consensus quality even under increased disruptions.

Engineering Consensus in Static Networks with Unknown Disruptors

Introduction to Distributed Control and Consensus Formation

In the context of distributed control systems, the shift from centralized control strategies to distributed ones is primarily motivated by the need to enhance scalability, flexibility, and eliminate single points of failure. However, this decentralization introduces vulnerabilities, especially in multi-agent systems where the lack of centralized oversight makes the network susceptible to disruptors. Traditionally, networks such as IoTs, mobile robotic systems, smart power grids, and wireless sensor networks embody these characteristics. Central to distributed control is the concept of consensus - a process through which nodes within the network reach a common agreement, essential for coordinated action and decision-making.

Addressing Disruptions in Consensus Algorithms

To tackle the problem of disruptions in consensus formation, standard approaches often require knowledge of the network’s topology and the number and behavior of disruptors. However, such information is not always available or reliable in real-world scenarios. Mean-Subsequence-Reduced (MSR) methods and their derivatives illustrate classical approaches that aim to ensure fault-resilience by excluding certain values from consideration during consensus iterations, relying on predefined knowledge of potential faults. This paper proposes an innovative consensus algorithm inspired by social dynamics, particularly the Deffuant Model, to achieve efficient and robust consensus without such prerequisites.

The Opinion Dynamics-inspired Disruption-tolerant Consensus (ODDI-C) Algorithm

The ODDI-C algorithm leverages the concept of social tolerance from the Deffuant Model, dynamically adjusting the level of tolerance based on the agents’ positions relative to a consensus opinion. This approach allows for the filtering out of extreme, potentially disruptive opinions without prior knowledge of the disruptors or the network structure. The algorithm’s novelty lies in its adaptability, which enables faster convergence compared to traditional MSR-type methods under a variety of scenarios.

• Dynamic Tolerance and Filtering: The core mechanism enables agents to ignore values from neighbors that are considered too extreme, based on dynamically adjusted tolerance levels. This adaptation ensures that the consensus process is less likely to be swayed by disruptive agents.
• Utilization of Median-based Z-scores: Instead of direct opinion values, the algorithm employs median-based z-scores to determine which opinions to consider during the consensus process. This method enhances the robustness of the consensus against outliers.

Experimental Validation and Comparative Analysis

Numerical experiments conducted to assess the performance of the ODDI-C algorithm demonstrate its effectiveness in achieving consensus under varying conditions of network connectivity and presence of disruptors. The results highlight ODDI-C’s superiority in terms of faster convergence and higher resilience compared to MSR. Furthermore, ODDI-C’s performance showcases its ability to maintain consensus quality even as the number of disruptors increases, evidencing its practical applicability to real-world distributed networks where the disruption landscape is unpredictable.

• Experiment on Fixed Number of Disruptors and Increasing Network Connectivity: Demonstrated that ODDI-C outperforms MSR algorithms, particularly at high connectivity levels.
• Fixed Connectivity and Increasing Number of Disruptors: Showed ODDI-C’s resilience by maintaining consensus quality even with a higher ratio of disruptors to compliant agents.

Implications and Future Directions

The introduction of the ODDI-C algorithm marks a significant step toward more resilient distributed control systems capable of countering disruption without reliance on exhaustive network information. Its foundation in social dynamics offers an interesting perspective on consensus formation, suggesting avenues for further research into adaptive and self-regulating algorithms in distributed systems.

Moving forward, exploring the integration of ODDI-C with broader network topologies, including dynamic networks where connections between nodes vary over time, could yield additional insights into enhancing distributed system resilience. Additionally, the adaptability of the ODDI-C algorithm to various types of disruptions—beyond those simulated in the numerical experiments—promises a fertile ground for extending the current work to encompass a wider range of real-world applications.

Conclusion

The research presented provides a novel approach to achieving consensus in distributed networks faced with the challenge of unknown disruptors. By borrowing concepts from the field of sociophysics, the ODDI-C algorithm not only enriches the toolkit available for designing resilient multi-agent systems but also opens new pathways for exploring the interplay between social dynamics and technological infrastructures.