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Decentralized Dynamic Event-triggered Output-feedback Control of Stochastic Non-triangular Interconnected Systems with Unknown Time-varying Sensor Sensitivity

Libei Sun, Yongduan Song, Maolong Lv

TL;DR

This work addresses decentralized dynamic event-triggered output-feedback control for stochastic nonlinear interconnected systems with non-triangular couplings and unknown time-varying sensor sensitivity. It introduces a novel coordinate transformation to linearize subsystem state relations, and couples it with a decentralized observer and a clock-based dynamic triggering mechanism to prevent Zeno behavior. The authors prove global asymptotic stability in probability for the closed-loop and establish a minimal inter-execution time, while preserving zero steady-state error in probability and reducing communication burden. A comprehensive simulation demonstrates convergence, robust performance under sensor uncertainty, and favorable trigger behavior compared to static or time-regulation-based schemes. The results advance practical, scalable control for complex stochastic networks with uncertain sensing, enabling reliable operation with intermittent communication.

Abstract

This study addresses the intricate challenge of decentralized output-feedback control for stochastic non-triangular nonlinear interconnected systems with unknown time-varying sensor sensitivity in a dynamic event-triggered context. The presence of stochastic disturbances, non-triangular structural uncertainties, and evolving sensor sensitivity distinguishes this problem of global asymptotic stability from conventional event-triggered control scenarios. Existing event-triggered control approaches with static event conditions encounter difficulties in simultaneously ensuring zero tracking/stabilization error and preventing the occurrence of Zeno behavior. In this work, we develop a novel solution to address this complex issue. Firstly, we establish a linear relationship between the state vector of each interconnected subsystem and two error vectors through a unique coordinate transformation. This transformation effectively handles the complexities introduced by non-triangular structural uncertainties. Secondly, we introduce a decentralized dynamic event-triggered output-feedback control strategy, which involves a state observer and a decentralized output-feedback controller. Unlike conventional event-triggered control methods with static event conditions, this strategy formulates a modified clock-based dynamic triggering mechanism by introducing an auxiliary variable that evolves based on predicted plant state values, while utilizing a clock variable to guarantee the existence of a positive lower bound on inter-execution times. Rigorous Lyapunov analysis confirms the global asymptotic stability in probability of the closed-loop system, with the states and the output of each local subsystem converging to the equilibrium at the origin in probability. Additionally, the existence of a minimal dwell-time between triggering instants is guaranteed.

Decentralized Dynamic Event-triggered Output-feedback Control of Stochastic Non-triangular Interconnected Systems with Unknown Time-varying Sensor Sensitivity

TL;DR

This work addresses decentralized dynamic event-triggered output-feedback control for stochastic nonlinear interconnected systems with non-triangular couplings and unknown time-varying sensor sensitivity. It introduces a novel coordinate transformation to linearize subsystem state relations, and couples it with a decentralized observer and a clock-based dynamic triggering mechanism to prevent Zeno behavior. The authors prove global asymptotic stability in probability for the closed-loop and establish a minimal inter-execution time, while preserving zero steady-state error in probability and reducing communication burden. A comprehensive simulation demonstrates convergence, robust performance under sensor uncertainty, and favorable trigger behavior compared to static or time-regulation-based schemes. The results advance practical, scalable control for complex stochastic networks with uncertain sensing, enabling reliable operation with intermittent communication.

Abstract

This study addresses the intricate challenge of decentralized output-feedback control for stochastic non-triangular nonlinear interconnected systems with unknown time-varying sensor sensitivity in a dynamic event-triggered context. The presence of stochastic disturbances, non-triangular structural uncertainties, and evolving sensor sensitivity distinguishes this problem of global asymptotic stability from conventional event-triggered control scenarios. Existing event-triggered control approaches with static event conditions encounter difficulties in simultaneously ensuring zero tracking/stabilization error and preventing the occurrence of Zeno behavior. In this work, we develop a novel solution to address this complex issue. Firstly, we establish a linear relationship between the state vector of each interconnected subsystem and two error vectors through a unique coordinate transformation. This transformation effectively handles the complexities introduced by non-triangular structural uncertainties. Secondly, we introduce a decentralized dynamic event-triggered output-feedback control strategy, which involves a state observer and a decentralized output-feedback controller. Unlike conventional event-triggered control methods with static event conditions, this strategy formulates a modified clock-based dynamic triggering mechanism by introducing an auxiliary variable that evolves based on predicted plant state values, while utilizing a clock variable to guarantee the existence of a positive lower bound on inter-execution times. Rigorous Lyapunov analysis confirms the global asymptotic stability in probability of the closed-loop system, with the states and the output of each local subsystem converging to the equilibrium at the origin in probability. Additionally, the existence of a minimal dwell-time between triggering instants is guaranteed.

Paper Structure

This paper contains 10 sections, 5 theorems, 49 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. State Observer Design
  4. Decentralized Continuous Output-feedback Control
  5. Decentralized Dynamic Event-triggered Output-feedback Control
  6. Design of A Modified Clock-based Dynamic Triggering Mechanism
  7. Discussion on the Design Philosophy and Merits of the Proposed Triggering Mechanism
  8. Decentralized Dynamic Event-triggered Control Scheme
  9. Simulation Verification
  10. Conclusion

Key Result

Lemma 1

(see chen2017global) For $p \in[1, \infty)$ and any $x_{i,k} \in \mathcal{R}$, $i=1, \cdots, N$, $k=1,\cdots,n_i$, the following inequality holds:

Figures (3)

  • Figure 1: A block diagram of the proposed decentralized control strategy with output and controller triggering.
  • Figure 2: The results of the proposed method. (a) The states $x_{i,k}$ and state estimates $\hat{x}_{i,k}$. (b) The output $y_{i}$. (c) The control input $u_i$. (d) The dynamic auxiliary variables $\Xi_{y_i}$ and $\Xi_{u_i}$.
  • Figure 3: The comparison results. (a) The triggering times of $u_i$ and $y_i$ under the proposed method. (b) The clock variables $\Pi_{y_i}$ and $\Pi_{u_i}$ under the proposed method. (c) The triggering times of $u_i$ and $y_i$ under the time-regulation-based method tang2022event . (d) The clock variables $\Pi_{y_i}$ and $\Pi_{u_i}$ under the time-regulation-based method tang2022event .

Theorems & Definitions (10)

  • Lemma 1
  • Remark 1
  • Remark 2
  • Lemma 2
  • Lemma 3
  • Remark 3
  • Remark 4
  • Theorem 1
  • Theorem 2
  • Remark 5