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Data-driven Dynamic Event-triggered Control

Tao Xu, Zhiyong Sun, Guanghui Wen, Zhisheng Duan

TL;DR

The paper addresses event-triggered control for unknown continuous-time linear systems with disturbances by introducing a data-driven dynamic ETM whose triggering function is updated online. The off-line data processing yields a simple LMI-based design for the feedback gain and ETM parameters, ensuring exponential ISS with respect to disturbances and a strictly positive minimum inter-event time, without requiring a prescribed timer. The framework is extended to uniform and logarithmic state quantization, preserving ISS properties under practical constraints. Simulations on an aircraft model validate the approach and demonstrate the impact of disturbances and quantization on performance and MIET, highlighting practical viability and efficiency relative to existing methods.

Abstract

This paper revisits the event-triggered control problem from a data-driven perspective, where unknown continuous-time linear systems subject to disturbances are taken into account. Using data information collected off-line instead of accurate system model information, a data-driven dynamic event-triggered control scheme is developed in this paper. The dynamic property is reflected by that the designed event-triggering function embedded in the event-triggering mechanism (ETM) is dynamically updated as a whole. Thanks to this dynamic design, a strictly positive minimum inter-event time (MIET) is guaranteed without sacrificing control performance. Specifically, exponential input-to-state stability (ISS) of the closed-loop system with respect to disturbances is achieved in this paper, which is superior to some existing results that only guarantee a practical exponential ISS property. The dynamic ETM is easy-to-implement in practical operation since all designed parameters are determined only by a simple data-driven linear matrix inequality (LMI), without additional complicated conditions as required in relevant literature. As quantization is the most common signal constraint in practice, the developed control scheme is further extended to the case where state transmission is affected by a uniform or logarithmic quantization effect. Finally, adequate simulations are performed to show the validity and superiority of the proposed control schemes.

Data-driven Dynamic Event-triggered Control

TL;DR

The paper addresses event-triggered control for unknown continuous-time linear systems with disturbances by introducing a data-driven dynamic ETM whose triggering function is updated online. The off-line data processing yields a simple LMI-based design for the feedback gain and ETM parameters, ensuring exponential ISS with respect to disturbances and a strictly positive minimum inter-event time, without requiring a prescribed timer. The framework is extended to uniform and logarithmic state quantization, preserving ISS properties under practical constraints. Simulations on an aircraft model validate the approach and demonstrate the impact of disturbances and quantization on performance and MIET, highlighting practical viability and efficiency relative to existing methods.

Abstract

This paper revisits the event-triggered control problem from a data-driven perspective, where unknown continuous-time linear systems subject to disturbances are taken into account. Using data information collected off-line instead of accurate system model information, a data-driven dynamic event-triggered control scheme is developed in this paper. The dynamic property is reflected by that the designed event-triggering function embedded in the event-triggering mechanism (ETM) is dynamically updated as a whole. Thanks to this dynamic design, a strictly positive minimum inter-event time (MIET) is guaranteed without sacrificing control performance. Specifically, exponential input-to-state stability (ISS) of the closed-loop system with respect to disturbances is achieved in this paper, which is superior to some existing results that only guarantee a practical exponential ISS property. The dynamic ETM is easy-to-implement in practical operation since all designed parameters are determined only by a simple data-driven linear matrix inequality (LMI), without additional complicated conditions as required in relevant literature. As quantization is the most common signal constraint in practice, the developed control scheme is further extended to the case where state transmission is affected by a uniform or logarithmic quantization effect. Finally, adequate simulations are performed to show the validity and superiority of the proposed control schemes.
Paper Structure (15 sections, 4 theorems, 57 equations, 5 figures, 1 table, 1 algorithm)

This paper contains 15 sections, 4 theorems, 57 equations, 5 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notation
  4. Problem formulation
  5. Main results
  6. Comparisons
  7. Dynamic ETMs with a prescribed timer or a dynamic internal variable
  8. A dynamic ETM with a prescribed timer and a dynamic internal variable
  9. Extensions
  10. Simulations
  11. Simulation results in the absence of quantization
  12. Simulation results in the presence of quantization
  13. Conclusions
  14. Proof of Theorem \ref{['th1']}
  15. Proof of Theorem \ref{['th2']}

Key Result

Theorem 1

Suppose that Assumptions as1-- as4 hold, and there exist proper positive constants $\alpha, \beta, \delta$, such that the following data-driven LMI holds Using the dynamic ETM (eq4)--(eq7), the event-based controller (eq8), and the data-driven feedback gain matrix (eq9), then,

Figures (5)

  • Figure 1: Implementation process of the proposed data-driven dynamic event-triggered control scheme, where the devices in the orange blocks are common in traditional control mode, and those in the green blocks are essential in the data-driven event-triggered control framework.
  • Figure 2: The trajectories of each component of the system state $x(t)$ under fixed $\bar{f}=100$ and different $\bar{d}$.
  • Figure 3: The evolution of the dynamic event-triggering function $f(t)$.
  • Figure 4: The evolution of each component of the system state $x(t)$ under fixed $\bar{f}_{u}=100$ and different $\theta$ in the presence of uniform quantization.
  • Figure 5: The evolution of each component of the system state $x(t)$ under fixed $\bar{f}_{l}=100$ and different $\theta$ in the presence of logarithmic quantization.

Theorems & Definitions (10)

  • Definition 1
  • Theorem 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Theorem 2
  • Lemma 1
  • Lemma 2
  • proof
  • proof