Research on Global Consensus of Stochastic Multi-Agent Systems Based on Robust Fuzzy Cooperative Strategy

Academic Background

In modern technological fields such as automation, robotics, network communication, intelligent transportation systems, and distributed decision-making, Multi-Agent Systems (MAS) play a crucial role. MAS can efficiently execute complex tasks and optimize resource allocation through the collaborative efforts of multiple agents. However, achieving global consensus in complex and uncertain environments is a significant challenge. These uncertainties include the inherent unpredictability of the agents themselves and external disturbances, particularly in stochastic environments where the behavioral patterns of agents and constantly changing environmental conditions make the realization of global consensus even more complex and difficult.

Existing control strategies mainly fall into two categories: model-based and model-free methods. Model-based methods, such as robust control, rely on precise models but face limitations due to uncertainties in practical applications. On the other hand, model-free methods, such as fuzzy control, effectively handle uncertainties but lack theoretical support for global performance and consistency guarantees. Therefore, developing a control strategy that combines the strengths of both approaches while mitigating their respective weaknesses is particularly important. This research context has driven the exploration of robust fuzzy control strategies, aiming to leverage the adaptability and uncertainty-handling capabilities of fuzzy control while incorporating the robustness features of model-based methods to provide a more comprehensive and reliable solution.

Source of the Paper

This paper was co-authored by Jiaxi Chen, Jitao Shen, Weisheng Chen, Junmin Li, and Shuai Zhang. The authors are affiliated with the School of Mathematics and Statistics, School of Aerospace Science and Technology, and the Science and Technology on Antennas and Microwave Laboratory at Xidian University. The paper was published in IEEE Transactions on Automation Science and Engineering in 2025.

Research Process and Results

Research Process

Part One: First-Order Stochastic Multi-Agent Systems

The study first focused on first-order stochastic multi-agent systems, designing a distributed robust fuzzy control protocol. The specific steps are as follows:

1. Model Construction: The dynamic model of the first-order stochastic multi-agent system was defined, including the state equations of the followers and the leader.
   
2. Controller Design: A hybrid control strategy based on a robust controller, fuzzy controller, and auxiliary controller was proposed, with smooth switching functions ensuring effectiveness and robustness across a global scope.
   
3. Lyapunov Function Design: A novel Lyapunov function was innovatively designed to ensure the stability of the closed-loop system.
   
4. Simulation Experiments: The practical effectiveness of the proposed algorithm was verified through simulation experiments.
   

Part Two: Second-Order Stochastic Multi-Agent Systems

The study was further extended to second-order stochastic multi-agent systems, where a distributed robust fuzzy control protocol was designed. The specific steps are as follows:

1. Model Construction: The dynamic model of the second-order stochastic multi-agent system was defined, including the state equations of the followers and the leader.
   
2. Controller Design: A hybrid control strategy based on a robust controller, fuzzy controller, and auxiliary controller was proposed, with smooth switching functions ensuring effectiveness and robustness across a global scope.
   
3. Lyapunov Function Design: A novel Lyapunov function was innovatively designed to ensure the stability of the closed-loop system.
   
4. Simulation Experiments: The practical effectiveness of the proposed algorithm was verified through simulation experiments.
   

Main Results

Part One: First-Order Stochastic Multi-Agent Systems

Through simulation experiments, the researchers verified that the proposed control algorithm effectively achieved tracking consensus between followers and the leader. The specific results are as follows:

1. Convergence of Tracking Errors: The simulation results showed that the tracking errors between the followers and the leader eventually converged to near zero, proving the achievement of consensus.
   
2. Stability of Input Signals: All input signals (control inputs, adaptive parameters, etc.) remained bounded, ensuring system stability and controllability.
   

Part Two: Second-Order Stochastic Multi-Agent Systems

Through simulation experiments, the researchers verified that the proposed control algorithm effectively achieved tracking consensus between followers and the leader. The specific results are as follows:

1. Convergence of Tracking Errors: The simulation results showed that the tracking errors between the followers and the leader eventually converged to near zero, proving the achievement of consensus.
   
2. Stability of Input Signals: All input signals (control inputs, adaptive parameters, etc.) remained bounded, ensuring system stability and controllability.
   

Conclusions and Value

This study successfully developed an advanced robust fuzzy distributed protocol that seamlessly integrates robust control and fuzzy control to address the global consensus problem in unknown multi-agent systems. The practical effectiveness of the protocol was significantly enhanced through a smooth switching function. The research provided a comprehensive design framework for robust fuzzy controllers in both first-order and second-order stochastic multi-agent systems. The innovative design of the Lyapunov function ensured system stability. Simulation experiments confirmed the practical effectiveness of the proposed algorithm, laying the foundation for future multi-agent applications.

Highlights of the Research

1. Innovative Control Strategy: The core innovation of this research lies in designing a robust fuzzy distributed protocol based on a smooth switching function, which not only combines the advantages of robust control and fuzzy control but also ensures the achievement of global consensus.
   
2. Broad Applicability: Unlike previous studies that focused only on nonlinear dynamic scenarios satisfying the global Lipschitz condition, this research relaxed this restriction, expanding to a wider and more complex range of unknown scenarios.
   
3. Novel Lyapunov Function: Different from traditional direct construction methods, this study innovatively designed a novel Lyapunov function based on the Lyapunov quadratic form concept to prove the stability of the closed-loop system.
   

Additional Valuable Information

The researchers noted that although the distributed algorithm demonstrated effectiveness in simulation experiments, its scalability in large-scale multi-agent systems still requires further evaluation. Future work should focus on comprehensive testing and theoretical analysis of larger-scale systems to ensure its efficiency and reliability in complex environments.

Through this study, we not only addressed the limitations of existing methods in handling uncertainties and disturbances but also advanced the theoretical understanding of control in multi-agent systems, paving the way for more efficient and reliable MAS.