Scalable Non-collaborative Linear Protocol Design for Homogeneous Multi-agent Systems

Основные понятия

This paper presents a class of continuous- and discrete-time homogeneous multi-agent systems for which scalable non-collaborative (fully distributed) linear protocols can be designed.

Аннотация

The paper focuses on identifying a class of continuous- and discrete-time multi-agent systems (MAS) for which a scalable non-collaborative (i.e., scale-free fully distributed) linear protocol design is developed. The authors have identified conditions on agent models that enable the design of scalable linear protocols. These conditions are necessary if the agents are single input and single output.
The key highlights and insights are:

For continuous-time MAS, the authors provide necessary conditions for the solvability of the scale-free state synchronization problem without localized collaborative information exchange. These conditions include the agent model being stabilizable, detectable, neutrally stable, minimum phase, and having a relative degree of 1.

Under these necessary conditions, the authors present a two-step protocol design for continuous-time MAS. The first step designs a pre-compensator to make the agent model left-invertible, and the second step designs a non-collaborative dynamical protocol for the left-invertible agents to achieve state synchronization.

For discrete-time MAS, the authors show that the necessary conditions are stabilizability, detectability, and neutral stability of the agent model. They then provide a scale-free non-collaborative linear protocol design using a stable observer with the CSS architecture.

The proposed protocols are shown to achieve state synchronization for any fixed communication graph and any number of agents, without requiring any knowledge about the communication network.

Статистика

None.

Цитаты

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Ключевые выводы из

Scale-free Non-collaborative Linear Protocol Design for A Class of Homogeneous Multi-agent Systems

by Zhenwei Liu,... в arxiv.org 04-16-2024

https://arxiv.org/pdf/2306.01582.pdf

Дополнительные вопросы

How can the proposed protocol designs be extended to handle more general agent models, such as those that are not minimum phase or have higher relative degrees

The proposed protocol designs can be extended to handle more general agent models by incorporating additional compensators or observers to address the specific characteristics of the agents. For agent models that are not minimum phase or have higher relative degrees, the design process may involve more complex transformations or compensations to ensure stability and convergence.
For non-minimum phase systems, additional pre-compensators or state transformations can be introduced to modify the system dynamics and achieve the desired performance. By carefully designing these compensators, it is possible to stabilize the system and enable synchronization even in the presence of non-minimum phase behavior.
Similarly, for agent models with higher relative degrees, the protocol design may involve the use of higher-order compensators or observers to handle the increased complexity of the system dynamics. By incorporating these additional elements into the protocol design, it is possible to extend the scalability and applicability of the proposed approach to a wider range of agent models.
Overall, by customizing the protocol design to suit the specific characteristics of the agent models, including non-minimum phase behavior or higher relative degrees, the proposed approach can be adapted to address a broader class of homogeneous multi-agent systems.

What are the potential limitations or drawbacks of the scale-free non-collaborative approach compared to collaborative protocols in terms of convergence rate or robustness to disturbances

The scale-free non-collaborative approach, while offering advantages in terms of fully distributed protocols and scalability, may have limitations compared to collaborative protocols in terms of convergence rate and robustness to disturbances.
One potential limitation of the scale-free non-collaborative approach is the convergence rate of the synchronization process. Collaborative protocols, which involve additional information exchange between agents, can potentially achieve faster convergence by leveraging more comprehensive information about the system dynamics. In contrast, the non-collaborative approach relies solely on local measurements and relative information, which may result in slower convergence rates, especially in complex or large-scale systems.
Another limitation is the robustness of the synchronization process to disturbances or uncertainties in the system. Collaborative protocols, by incorporating additional information exchange, may exhibit greater robustness to disturbances as agents can adapt and adjust their behaviors based on shared information. In contrast, the non-collaborative approach may be more susceptible to disturbances, as agents operate based on local measurements without the benefit of collaborative information exchange.
Overall, while the scale-free non-collaborative approach offers advantages in terms of distributed and scalable protocol design, it is important to consider the trade-offs in convergence rate and robustness compared to collaborative protocols.

Can the insights from this work be applied to other distributed control problems beyond multi-agent synchronization, such as distributed optimization or distributed estimation

The insights from this work on scale-free non-collaborative protocol design for multi-agent systems can be applied to other distributed control problems beyond synchronization.
For distributed optimization problems, the concept of scale-free protocol design can be utilized to develop distributed algorithms that do not rely on a centralized coordinator or global information. By designing protocols that are fully distributed and scalable, it is possible to optimize system performance while maintaining the autonomy and decentralization of the agents.
In the context of distributed estimation, the principles of non-collaborative protocol design can be leveraged to develop distributed estimation algorithms that operate based on local measurements and relative information exchange. By ensuring scalability and fully distributed operation, these algorithms can enable accurate estimation in large-scale systems without the need for centralized processing.
Overall, the insights and methodologies from this work can be extended to various distributed control problems, providing a framework for designing efficient and scalable protocols for a wide range of applications beyond multi-agent synchronization.