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Event-Triggered Memory Control for Interval Type-2 Fuzzy Heterogeneous Multi-Agent Systems

Sen Kong

TL;DR

The paper tackles robust control for heterogeneous multi-agent systems (MASs) with nonlinear uncertainties and limited inter-agent communication by developing a memory-based dynamic event-triggered mechanism (DETM) within discrete-time interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy models. It introduces a non-PDC, memory-rich control strategy and a dynamic threshold $\Delta_i$ to reduce data transmissions while maintaining performance, culminating in a less conservative LMI-based stability condition derived from a Kronecker-product augmented system and a Lyapunov function $V(t)=\mathbf{x}^T(t)P\mathbf{x}(t)$. Controller gains are computed as $\tilde{K}_{s_i}^i = X_{s_i}^{i^{-1}} \tilde{Y}_{s_i}^i$, with augmented histories $\tilde{x}_i(t)$, $\tilde{e}_i(t)$, and $\tilde{\delta}_i(t_k^i)$ to capture memory effects. Numerical simulations on a 4-agent heterogeneous IT2 T-S fuzzy MAS demonstrate consensus and stability with significantly fewer triggers, validating the approach for resource-constrained real-world MAS applications.

Abstract

This study explores the design of a memory-based dynamic event-triggered mechanisms (DETM) scheme for heterogeneous multi-agent systems (MASs) characterized by interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy models. To address the complex nonlinear uncertainties inherent in such systems, discrete IT2 T-S fuzzy models are employed to accurately capture system dynamics. In response to the limitations on communication resources and computational capabilities within MASs, this research introduces a distributed DETM approach based on a dynamic threshold method. This mechanism effectively minimizes unnecessary communication while maintaining robust performance. The proposed memory-based control strategy not only reduces the conservatism associated with controller design conditions but also enhances overall controller performance. Furthermore, leveraging a non-parallel distributed compensation (non-PDC) strategy, a novel derivation method is developed for controller design conditions that significantly decreases conservatism. This leads to sufficient conditions for the asymptotic stability of the closed-loop system. The designed distributed event-triggered controllers improve the overall performance of MASs, as evidenced by numerical simulations that validate the effectiveness of the proposed approach. Overall, these findings advance the state-of-the-art in control strategies for heterogeneous MASs, offering practical solutions for real-world applications where resource constraints are critical.

Event-Triggered Memory Control for Interval Type-2 Fuzzy Heterogeneous Multi-Agent Systems

TL;DR

The paper tackles robust control for heterogeneous multi-agent systems (MASs) with nonlinear uncertainties and limited inter-agent communication by developing a memory-based dynamic event-triggered mechanism (DETM) within discrete-time interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy models. It introduces a non-PDC, memory-rich control strategy and a dynamic threshold to reduce data transmissions while maintaining performance, culminating in a less conservative LMI-based stability condition derived from a Kronecker-product augmented system and a Lyapunov function . Controller gains are computed as , with augmented histories , , and to capture memory effects. Numerical simulations on a 4-agent heterogeneous IT2 T-S fuzzy MAS demonstrate consensus and stability with significantly fewer triggers, validating the approach for resource-constrained real-world MAS applications.

Abstract

This study explores the design of a memory-based dynamic event-triggered mechanisms (DETM) scheme for heterogeneous multi-agent systems (MASs) characterized by interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy models. To address the complex nonlinear uncertainties inherent in such systems, discrete IT2 T-S fuzzy models are employed to accurately capture system dynamics. In response to the limitations on communication resources and computational capabilities within MASs, this research introduces a distributed DETM approach based on a dynamic threshold method. This mechanism effectively minimizes unnecessary communication while maintaining robust performance. The proposed memory-based control strategy not only reduces the conservatism associated with controller design conditions but also enhances overall controller performance. Furthermore, leveraging a non-parallel distributed compensation (non-PDC) strategy, a novel derivation method is developed for controller design conditions that significantly decreases conservatism. This leads to sufficient conditions for the asymptotic stability of the closed-loop system. The designed distributed event-triggered controllers improve the overall performance of MASs, as evidenced by numerical simulations that validate the effectiveness of the proposed approach. Overall, these findings advance the state-of-the-art in control strategies for heterogeneous MASs, offering practical solutions for real-world applications where resource constraints are critical.

Paper Structure

This paper contains 5 sections, 2 theorems, 49 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Model Description and Problem Formulation
  3. Main Results
  4. Simulation Studies
  5. Conclusions

Key Result

Lemma 1

ref77 For any matrices $\mathbb{L}_{l_i s_i}^i$, $\Psi$, $\mathbb{R}_{l_i s_i}^i > 0$, and constants $m_{l_{i'}}^{i'}, n_{s_{i"}}^{i"} \in [0, 1]$, the following matrix inequality holds:

Figures (5)

  • Figure 1: The communication topology of the multi-agent system.
  • Figure 2: The event triggered conditions of the multi-agent system.
  • Figure 3: The state $x_1$ responses of the MAS.
  • Figure 4: The state $x_2$ responses of the MAS.
  • Figure 5: The control signal $u$ responses of the MAS.

Theorems & Definitions (2)

  • Lemma 1
  • Theorem 1