Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Model-Based Event-Triggered Implementation of Hybrid Controllers Using Finite-Time Convergent Observers

Xuanzhi Zhu, Pedro Casau, Carlos Silvestre

Abstract

In this paper, we explore the conditions for asymptotic stability of the hybrid closed-loop system resulting from the interconnection of a nonlinear plant, an intelligent sensor that generates finite-time convergent estimates of the plant state, and a controller node that receives opportunistic samples from the sensor node when certain model-based event-triggering conditions are met. The proposed method is endowed with a degree of separation, in the sense that the controller design is independent of the sensor design. This is achieved under mild regularity conditions imposed on the hybrid closed-loop system and the existence of persistently flowing solutions. We demonstrate the versatility of the method by implementing it on: 1) a sampled-data controller for regulation of linear plants; 2) a synergistic controller for attitude stabilization of rigid bodies. The effectiveness of these novel controllers is demonstrated through numerical simulations.

Model-Based Event-Triggered Implementation of Hybrid Controllers Using Finite-Time Convergent Observers

Abstract

In this paper, we explore the conditions for asymptotic stability of the hybrid closed-loop system resulting from the interconnection of a nonlinear plant, an intelligent sensor that generates finite-time convergent estimates of the plant state, and a controller node that receives opportunistic samples from the sensor node when certain model-based event-triggering conditions are met. The proposed method is endowed with a degree of separation, in the sense that the controller design is independent of the sensor design. This is achieved under mild regularity conditions imposed on the hybrid closed-loop system and the existence of persistently flowing solutions. We demonstrate the versatility of the method by implementing it on: 1) a sampled-data controller for regulation of linear plants; 2) a synergistic controller for attitude stabilization of rigid bodies. The effectiveness of these novel controllers is demonstrated through numerical simulations.

Paper Structure

This paper contains 12 sections, 11 theorems, 49 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Motivations
  4. Challenges and approaches
  5. Contributions
  6. Preliminaries & Notation
  7. Problem Setup
  8. Main Results
  9. Application
  10. Implementation of a sampled-data controller
  11. Implementation of a synergistic controller
  12. Conclusion

Key Result

Lemma 1

Given sets $\mathcal{X}_{}\subset\mathbb{R}^{n}$ and $\mathcal{Y}_{}\subset\mathbb{R}^{m}$, a function ${g}:\mathcal{X}_{}\times\mathcal{Y}_{}\to\mathbb{R}^{}$, and a set-valued mapping $\Pi_{}:\mathbb{R}^{n}\rightrightarrows\mathbb{R}^{m}$, then $\inf_{x\in\mathcal{X}_{},y\in\Pi_{}(x)} {g}(x,y) = \

Figures (3)

  • Figure 1: A graphical illustration of the nominal system $\mathcal{H}_{0}$ in \ref{['eqn:Hmc0']} (upper left), the closed-loop system $\mathcal{H}_{}$ in \ref{['eqn:closedloop']} (bottom), and the reduced system $\mathcal{H}_{}'$ after finite-time convergence of the sensor dynamics (upper right). Smaller shaded rectangle: controller node. Larger shaded rectangle: sensor node. In $\mathcal{H}_{}$, the replicas of $\mathcal{H}_{c}$ are synchronized and the replicas of $\mathcal{H}_{s}$ are synchronized.
  • Figure 2: Comparison between continuous-time evolution and the corresponding inter-transmission time of solutions to the unperturbed/perturbed closed-loop systems using our proposed controller and the controllers (a)-(c) in Section \ref{['sec:application linear']}. Vertical axes are in log scale. Left column of figures: plots for the unperturbed closed-loop systems. Right column of figures: plots for the perturbed closed-loop systems. Top row of figures: continuous-time evolution of the distance of solutions to $\mathcal{A}_{}$ in Corollary \ref{['coro:app1']}. Bottom row of figures: inter-transmission time for the sensor-to-controller communication channels.
  • Figure 3: Comparison between continuous-time evolution and the corresponding inter-transmission time of solutions to the unperturbed/perturbed closed-loop systems using our proposed controller and the controllers (a)-(c) in Section \ref{['sec:application nonlinear']}. Vertical axes are in log scale. Left column of figures: plots for the unperturbed closed-loop systems. Right column of figures: plots for the perturbed closed-loop systems. Top row of figures: continuous-time evolution of the distance of solutions to $\mathcal{A}_{}$ in Corollary \ref{['coro:app2']}. Bottom row of figures: inter-transmission time for the sensor-to-controller communication channels.

Theorems & Definitions (21)

  • Definition 1: Goebel2012, Ricardo2021, Li2019
  • Remark 1
  • Definition 2: Bernard2020
  • Definition 3: Rockafellar1998
  • Remark 2
  • Definition 4: Inspired by Postoyan2015 and Goebel2012
  • Lemma 1
  • Remark 3
  • Remark 4
  • Lemma 2
  • ...and 11 more