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Cloud-mediated self-triggered synchronization of a general linear multi-agent system over a directed graph

Takumi Namba, Kiyotsugu Takaba

TL;DR

The paper addresses energy- and bandwidth-efficient synchronization of a network of high-order LTI agents connected by a directed graph, by leveraging cloud-mediated self-triggered control. It develops a controller with relative-state feedback, uses predictions of neighbor states computed from cloud data, and enforces a decaying triggering threshold based on tight bounds on matrix exponentials to handle exponential dynamics. A key contribution is proving non-Zeno behavior and uniform ultimate boundedness of the synchronization error, with explicit conditions on the gain $F$ and the triggering rule that guarantee performance. The approach is validated numerically on a 4-agent system, showing bounded synchronization to a common trajectory while maintaining non-accumulating cloud accesses, highlighting practical relevance for scenarios with limited instantaneous inter-agent communication.

Abstract

This paper proposes a self-triggered synchronization control method of a general high-order linear time-invariant multi-agent system through a cloud repository. In the cloud-mediated self-triggered control, each agent asynchronously accesses the cloud repository to get past information on its neighboring agents. Then, the agent predicts future behaviors of its neighbors as well as of its own, and locally determines its next access time to the cloud repository. In the case of a general high-order linear agent dynamics, each agent has to estimate exponential evolution of its trajectory characterized by eigenvalues of a system matrix, which is different from single/double integrator or first-order linear agents. Our proposed method deals with exponential behaviors of the agents by tightly evaluating the bounds on matrix exponentials. Based on these bound, we design the self-triggered controller through a cloud which achieves bounded state synchronization of the closed-loop system without exhibiting any Zeno behaviors. The effectiveness of the proposed method is demonstrated through the numerical simulation.

Cloud-mediated self-triggered synchronization of a general linear multi-agent system over a directed graph

TL;DR

The paper addresses energy- and bandwidth-efficient synchronization of a network of high-order LTI agents connected by a directed graph, by leveraging cloud-mediated self-triggered control. It develops a controller with relative-state feedback, uses predictions of neighbor states computed from cloud data, and enforces a decaying triggering threshold based on tight bounds on matrix exponentials to handle exponential dynamics. A key contribution is proving non-Zeno behavior and uniform ultimate boundedness of the synchronization error, with explicit conditions on the gain and the triggering rule that guarantee performance. The approach is validated numerically on a 4-agent system, showing bounded synchronization to a common trajectory while maintaining non-accumulating cloud accesses, highlighting practical relevance for scenarios with limited instantaneous inter-agent communication.

Abstract

This paper proposes a self-triggered synchronization control method of a general high-order linear time-invariant multi-agent system through a cloud repository. In the cloud-mediated self-triggered control, each agent asynchronously accesses the cloud repository to get past information on its neighboring agents. Then, the agent predicts future behaviors of its neighbors as well as of its own, and locally determines its next access time to the cloud repository. In the case of a general high-order linear agent dynamics, each agent has to estimate exponential evolution of its trajectory characterized by eigenvalues of a system matrix, which is different from single/double integrator or first-order linear agents. Our proposed method deals with exponential behaviors of the agents by tightly evaluating the bounds on matrix exponentials. Based on these bound, we design the self-triggered controller through a cloud which achieves bounded state synchronization of the closed-loop system without exhibiting any Zeno behaviors. The effectiveness of the proposed method is demonstrated through the numerical simulation.
Paper Structure (14 sections, 4 theorems, 36 equations, 6 figures, 2 tables, 2 algorithms)

This paper contains 14 sections, 4 theorems, 36 equations, 6 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Agent Model
  4. Communication Model
  5. Cloud Repository
  6. Accessibility Graph
  7. Problem Description
  8. Cloud-mediated Self-triggered Synchronization
  9. Controller Design
  10. Guarantee of Non-Zeno Behavior
  11. Analysis on Bounded Consensus
  12. Algorithm
  13. Numerical Simulation
  14. Concluding Remarks

Key Result

Lemma 1

Assume that is satisfied for all $t\in\left[t_{0},t_{f}\right[,~i\in\mathcal{V}$, $t_{0}<t_{f}$, where $t_{0}$ and $t_{f}$ are arbitrary. Then, the following inequalities hold. where the scaler-valued functions $\eta(t)$ and $\mu_{j}(t)$ are defined by with $\beta_{i}:=\|[L\otimes F]_{i}\|$, $\mathcal{B}':=(I_{N}-\mathds{1}_N\mathds{\phi}^{\sf T})\otimes B$, and $\eta_{0}\geq\|\delta(t_{0})\|$

Figures (6)

  • Figure 1: Communication model
  • Figure 2: Illustration of the relation among $t_{i}^{l_{i}}$, $t_{i}^{l_{i}+1}$, and $\tau_{i}^{\star}$
  • Figure 3: Accessibility graph
  • Figure 4: States $x_{i}$
  • Figure 5: Synchronization error $\|\delta(t)\|$
  • ...and 1 more figures

Theorems & Definitions (15)

  • Remark 1
  • Remark 2
  • Lemma 1
  • Proof
  • Remark 3: Choice of the feedback gains
  • Lemma 2
  • Proof
  • Remark 4
  • Remark 5
  • Remark 6
  • ...and 5 more