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Stabilization of singularly perturbed networked control systems over a single channel

Weixuan Wang, Alejandro I. Maass, Dragan Nešić, Ying Tan, Romain Postoyan, W. P. M. H. Heemels

Abstract

This paper studies the emulation-based stabilization of nonlinear networked control systems with two time scales. We address the challenge of using a single communication channel for transmitting both fast and slow variables between the plant and the controller. A novel dual clock mechanism is proposed to schedule transmissions for this purpose. The system is modeled as a hybrid singularly perturbed dynamical system, and singular perturbation analysis is employed to determine individual maximum allowable transmission intervals for both fast and slow variables, ensuring semi-global practical asymptotic stability. Enhanced stability guarantees are also provided under stronger assumptions. The efficacy of the proposed method is illustrated through a numerical example.

Stabilization of singularly perturbed networked control systems over a single channel

Abstract

This paper studies the emulation-based stabilization of nonlinear networked control systems with two time scales. We address the challenge of using a single communication channel for transmitting both fast and slow variables between the plant and the controller. A novel dual clock mechanism is proposed to schedule transmissions for this purpose. The system is modeled as a hybrid singularly perturbed dynamical system, and singular perturbation analysis is employed to determine individual maximum allowable transmission intervals for both fast and slow variables, ensuring semi-global practical asymptotic stability. Enhanced stability guarantees are also provided under stronger assumptions. The efficacy of the proposed method is illustrated through a numerical example.

Paper Structure

This paper contains 20 sections, 75 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem setting
  3. Plant ($\mathcal{P}$) and Controller ($\mathcal{C}$)
  4. Network ($\mathcal{N}$)
  5. A hybrid model for the SPNCS
  6. Clock Mechanism
  7. Hybrid model
  8. Auxiliary systems
  9. Change of coordinates
  10. Boundary layer system and reduced system of $\mathcal{H}_1$
  11. Emulation design framework
  12. Semi-global practical asymptotic stability
  13. Uniform global asymptotic/exponential stability
  14. Further stability results
  15. Special case: linear time invariant systems
  16. ...and 5 more sections

Figures (2)

  • Figure 1: NCS Block Diagram
  • Figure 2: Flow set and jump set