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NN-ETM: Enabling safe neural network-based event-triggering mechanisms for consensus problems

Irene Perez-Salesa, Rodrigo Aldana-Lopez, Carlos Sagues

TL;DR

The work tackles reducing communication in distributed consensus while preserving performance guarantees by decoupling the ETM design from the consensus protocol through input-to-state stability analysis. It introduces NN-ETM, a neural-network-based event-triggering mechanism that adapts triggering thresholds locally while maintaining a bounded consensus error and avoiding Zeno behavior. The authors provide ISS/ISpS-based guarantees for both linear and nonlinear consensus scenarios, and present a training-and-evaluation pipeline that balances error and communication via a tractable cost. The approach offers a practical, general framework for safe, data-driven ETMs in multi-agent networks with potential broad impact for resource-constrained distributed control.

Abstract

Event-triggering mechanisms (ETM) have been developed for consensus problems to reduce communication while ensuring performance guarantees, but their design has grown increasingly complex by incorporating the agent's local and neighbor information. This typically results in ad-hoc solutions, which may only work for the consensus protocol under consideration. We aim to safely incorporate neural networks in the ETM to provide a general solution while guaranteeing performance. To decouple the stability analysis of the consensus protocol from the abstraction of the neural network, we derive design criteria for the consensus and ETM pair, allowing independent analysis of each element under mild constraints. Then, we propose NN-ETM, a novel ETM featuring a neural network, to optimize communication while preserving the stability guarantees of the consensus protocol.

NN-ETM: Enabling safe neural network-based event-triggering mechanisms for consensus problems

TL;DR

The work tackles reducing communication in distributed consensus while preserving performance guarantees by decoupling the ETM design from the consensus protocol through input-to-state stability analysis. It introduces NN-ETM, a neural-network-based event-triggering mechanism that adapts triggering thresholds locally while maintaining a bounded consensus error and avoiding Zeno behavior. The authors provide ISS/ISpS-based guarantees for both linear and nonlinear consensus scenarios, and present a training-and-evaluation pipeline that balances error and communication via a tractable cost. The approach offers a practical, general framework for safe, data-driven ETMs in multi-agent networks with potential broad impact for resource-constrained distributed control.

Abstract

Event-triggering mechanisms (ETM) have been developed for consensus problems to reduce communication while ensuring performance guarantees, but their design has grown increasingly complex by incorporating the agent's local and neighbor information. This typically results in ad-hoc solutions, which may only work for the consensus protocol under consideration. We aim to safely incorporate neural networks in the ETM to provide a general solution while guaranteeing performance. To decouple the stability analysis of the consensus protocol from the abstraction of the neural network, we derive design criteria for the consensus and ETM pair, allowing independent analysis of each element under mild constraints. Then, we propose NN-ETM, a novel ETM featuring a neural network, to optimize communication while preserving the stability guarantees of the consensus protocol.
Paper Structure (23 sections, 6 theorems, 42 equations, 3 figures, 1 algorithm)

This paper contains 23 sections, 6 theorems, 42 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Design Criteria for ETM in Consensus
  4. Input-to-State Stability
  5. Interconnection of ISS consensus and ETM
  6. NN-ETM: Neural Network-Based Event-Triggering Mechanism
  7. NN-ETM Structure
  8. Neural Network Architecture
  9. Training the NN-ETM
  10. Parameter Sharing and Scalability
  11. Generation of Agents' Reference Signals
  12. Cost Function
  13. Fuzzy Event-Triggering Mechanism
  14. Weight Initialization
  15. ISS Consensus under NN-ETM
  16. ...and 8 more sections

Key Result

Theorem 1

Consider an event-triggered consensus protocol eq:consensus-ev-vec with disagreement dynamics eq:error-dyn. Then, there exists $\xi\geq 0$ such that for all initial conditions $\mathbf{x}(0)$, the consensus error is bounded $\forall t\geq 0$ with $\limsup_{t\to\infty} \|\mathbf{x}(t)\| \leq \xi$, if

Figures (3)

  • Figure 1: The event-triggered consensus problem can be globally viewed as the interaction between two interconnected blocks. We derive design criteria for each block to ensure stability guarantees for the interconnection.
  • Figure 2: Error $\mathcal{E}_r$ and communication rate $\mathcal{C}$ for NN-ETMs trained with different values of $\lambda$ in the cost function. The parameter $\lambda$ decides the trade-off between error and communication.
  • Figure 3: Example of consensus simulation and evolution of the learned variable $\eta_i(t)$ in the NN-ETM for each of the agents $i \in \mathcal{V}$. Adaptive behavior of $\eta_i(t)$ is achieved, which depends on the local observations of each agent.

Theorems & Definitions (15)

  • Definition 1
  • Theorem 1: Design Criteria
  • proof
  • Proposition 1: Performance of the ETM in \ref{['eq:send:on:delta']}
  • proof
  • Proposition 2: Minimum inter-event time for \ref{['eq:send:on:delta']}
  • proof
  • Corollary 1: Guarantees for NN-ETM
  • proof
  • Remark 1
  • ...and 5 more