Necessary and Sufficient Conditions for Scale-Free State Synchronization of Homogeneous Multi-Agent Systems

核心概念

Necessary and sufficient conditions for achieving scale-free state synchronization of homogeneous multi-agent systems via linear dynamic non-collaborative protocols, with and without utilizing local bounds on neighborhoods.

要約

The paper investigates the scale-free state synchronization problem for homogeneous multi-agent systems (MAS) in both continuous-time and discrete-time settings. It provides necessary and sufficient conditions for the existence of solutions to this problem.
Key highlights:

For continuous-time MAS without local bounds, necessary conditions are: stabilizability, detectability, neutral stability, minimum-phase, and relative degree 1. Sufficient conditions relax the minimum-phase requirement.
For continuous-time MAS with local bounds, necessary and sufficient conditions are: stabilizability, detectability, and neutral stability.
For discrete-time MAS without local bounds, scale-free synchronization is not possible except for asymptotically stable agents.
For discrete-time MAS with local bounds, necessary and sufficient conditions are: stabilizability, detectability, and neutral stability.
The paper shows that the availability of local bounds on neighborhoods plays a key role in achieving scale-free synchronization, especially in the discrete-time case where it becomes necessary. The results provide insights into the design of scale-free protocols for multi-agent systems.

統計

None.

引用

None.

抽出されたキーインサイト

The role of local bounds on neighborhoods in the network for scale-free state synchronization of multi-agent systems

by Anton A. Sto... 場所 arxiv.org 04-09-2024

https://arxiv.org/pdf/2310.02571.pdf

深掘り質問

How can the scale-free synchronization problem be extended to heterogeneous multi-agent systems

The scale-free synchronization problem can be extended to heterogeneous multi-agent systems by considering agents with different dynamics, such as different state-space models or different control inputs. In this case, the challenge lies in designing a protocol that can achieve synchronization despite the heterogeneity in the agents. One approach is to develop adaptive protocols that can adjust to the varying dynamics of the agents. By incorporating adaptive mechanisms into the protocol design, the system can adapt to the differences among agents and still achieve synchronization. Additionally, incorporating robust control techniques can help in handling the uncertainties and variations present in heterogeneous multi-agent systems.

What are the implications of the neutrally stable condition on the practical implementation of scale-free protocols

The neutrally stable condition has significant implications for the practical implementation of scale-free protocols. Neutrally stable systems have invariant zeros on the imaginary axis, which means that they do not exhibit exponential growth or decay. In the context of scale-free synchronization, the neutrally stable condition ensures that the system does not diverge or converge too quickly, allowing for a balanced and stable synchronization process. This condition is crucial for maintaining stability and preventing oscillations or instability in the synchronization of multi-agent systems. Implementing neutrally stable protocols ensures robust and reliable synchronization performance across different network topologies and agent configurations.

Can the scale-free synchronization problem be solved using nonlinear protocols without the neutrally stable condition

The scale-free synchronization problem can be solved using nonlinear protocols without the neutrally stable condition. Nonlinear protocols offer more flexibility and adaptability in handling complex dynamics and uncertainties in multi-agent systems. By incorporating nonlinear control techniques such as adaptive control, sliding mode control, or neural network-based control, it is possible to achieve scale-free synchronization without the strict requirement of neutrally stable agents. These nonlinear protocols can provide robustness against disturbances, uncertainties, and variations in the system, making them suitable for achieving synchronization in diverse and challenging environments.