Performance Comparison of Time-Triggered and Event-Triggered Consensus Control in Multi-Agent Systems

Core Concepts

For a multi-agent system with single-integrator dynamics, time-triggered control provably outperforms event-triggered control beyond a certain number of agents in terms of the long-term average quadratic deviation from consensus.

Abstract

The article analyzes and compares the performance of time-triggered control (TTC) and event-triggered control (ETC) schemes for a multi-agent system (MAS) with single-integrator dynamics. The authors consider an undirected connected communication graph without delays, and use the long-term average of the quadratic deviation from consensus as the performance measure.
The key findings are:

The authors show that TTC provably outperforms ETC beyond a certain number of agents in the MAS. This is in contrast to the often presumed superiority of ETC over TTC.

The authors derive the asymptotic order of the performance measure under both TTC and ETC, providing further insights into the cost relationship for large numbers of agents.

The authors demonstrate that transferring an event-triggering scheme from the single-loop to the multi-agent setting can lead to a loss of the often presumed superiority of ETC over TTC. This suggests that the design of performant decentralized ETC schemes can pose additional challenges compared to the single-loop case.

The authors consider an optimal control input class that resets all agents instantaneously to consensus at each triggering instant. This renders the control architecture distributed, and the analysis holds for any scheme within this class.

Overall, the article provides a fundamental performance comparison of TTC and ETC in a distributed multi-agent consensus setting, uncovering new phenomena that differ from the single-loop case.

Stats

The long-term average quadratic deviation from consensus under TTC is given by $J_{TT}(T_{TT}) = |\mathcal{E}| \cdot \frac{T_{TT}^2}{2}$, where $|\mathcal{E}|$ is the number of edges in the communication graph.
The asymptotic order of the expected inter-event time under ETC is $E[T_{ET}(1)] \sim \frac{1}{2 \ln N}$, where $N$ is the number of agents.
The asymptotic order of the variance of the inter-event time under ETC is $V[T_{ET}(1)] \sim \frac{\pi^2}{24 (\ln N)^4}$.

Quotes

"For this setup, ETC is not always superior to TTC, even without considering packet loss or transmission delays."
"The existence of such a critical number of agents is of interest by itself."
"This article thereby demonstrates that the design of performant decentralized ETC schemes can pose additional challenges compared to the analogue non-cooperative NCS case."

Key Insights Distilled From

Time- versus event-triggered consensus of a single-integrator multi-agent system

by Davi... at arxiv.org 05-01-2024

https://arxiv.org/pdf/2303.11097.pdf

Deeper Inquiries

How would the performance comparison between TTC and ETC change if the communication graph is not fully connected or if there are communication delays

In the context of the provided analysis, the performance comparison between Time-Triggered Control (TTC) and Event-Triggered Control (ETC) would change if the communication graph is not fully connected or if there are communication delays.

Non-Fully Connected Communication Graph:

In a non-fully connected communication graph, where not all agents can directly communicate with each other, the performance of both TTC and ETC may be affected.
For TTC, the constant inter-event time may lead to inefficiencies in communication between agents that are not directly connected, potentially causing delays in achieving consensus.
ETC, on the other hand, may face challenges in triggering transmissions effectively across the network, especially if the triggering conditions are based on local information only. This could result in suboptimal performance compared to a fully connected graph.

Communication Delays:

Introducing communication delays can significantly impact the performance of both TTC and ETC in multi-agent systems.
For TTC, delays can lead to synchronization issues and inconsistencies in the timing of transmissions, affecting the overall control performance and potentially causing deviations from the desired consensus state.
In the case of ETC, communication delays can disrupt the triggering mechanism, leading to suboptimal decisions on when to transmit information. This can result in increased deviations from consensus and reduced control performance.

In summary, non-fully connected communication graphs and communication delays can introduce additional challenges and complexities in the performance comparison between TTC and ETC in multi-agent systems, potentially altering the superiority of one control scheme over the other.

What other performance measures, beyond the quadratic deviation from consensus, could be considered to further understand the tradeoffs between TTC and ETC in multi-agent systems

To further understand the tradeoffs between Time-Triggered Control (TTC) and Event-Triggered Control (ETC) in multi-agent systems beyond the quadratic deviation from consensus, several alternative performance measures could be considered:

Communication Efficiency: Evaluate the efficiency of communication utilization under TTC and ETC, considering factors such as the amount of data transmitted, bandwidth usage, and network congestion. This measure can provide insights into the communication overhead of each control scheme.

Robustness to Network Changes: Assess how well TTC and ETC adapt to changes in the communication network topology, such as node failures or dynamic network structures. A performance measure that captures the resilience of each scheme to network variations can be valuable.

Energy Consumption: Analyze the energy consumption of agents under TTC and ETC, taking into account the frequency of transmissions and the computational load of triggering mechanisms. Comparing the energy efficiency of both control schemes can provide insights into their sustainability.

Scalability: Evaluate how well TTC and ETC scale with an increasing number of agents in the system. A performance measure that considers the scalability of each scheme in terms of computational complexity and communication overhead can help understand their applicability to larger multi-agent systems.

By incorporating these additional performance measures, a more comprehensive understanding of the tradeoffs between TTC and ETC in multi-agent systems can be achieved, enabling informed decision-making in selecting the most suitable control scheme for specific applications.

Can the insights from this analysis be extended to more general multi-agent coordination problems beyond consensus, such as formation control or task allocation

The insights from the analysis of Time-Triggered Control (TTC) and Event-Triggered Control (ETC) in the context of consensus problems can be extended to more general multi-agent coordination problems beyond consensus, such as formation control or task allocation.

Formation Control:

In formation control, where agents aim to maintain a specific geometric arrangement, the principles of TTC and ETC can be applied to synchronize the movements of agents and achieve the desired formation.
The performance comparison between TTC and ETC can help in determining which control scheme is more effective in maintaining formation stability, optimizing communication, and adapting to changes in the formation structure.

Task Allocation:

For task allocation among multiple agents, the concepts of TTC and ETC can be utilized to coordinate the assignment of tasks based on local and global information.
By extending the analysis to task allocation scenarios, the tradeoffs between TTC and ETC in terms of task completion time, resource utilization, and coordination efficiency can be evaluated.

Resource Management:

The insights gained from the comparison of TTC and ETC performance can be leveraged in resource management scenarios where multiple agents need to share resources efficiently.
By applying the principles of TTC and ETC to resource allocation and scheduling, optimal utilization of resources, minimization of conflicts, and maximization of system performance can be achieved.

Overall, the analysis of TTC and ETC in multi-agent systems can serve as a foundation for addressing a wide range of coordination problems, providing valuable insights into the design and implementation of control strategies for various collaborative tasks.