Delayed point control of a reaction–diffusion PDE under discrete-time point measurements

Anton Selivanov, Emilia Fridman

Research output: Contribution to journalArticlepeer-review

Abstract

We consider stabilization problem for reaction–diffusion PDEs with point actuations subject to a known constant delay. The point measurements are sampled in time and transmitted through a communication network with a time-varying delay. To compensate the input delay, we construct an observer for the future value of the state. Using a time-varying observer gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The convergence conditions are obtained using a Lyapunov–Krasovskii functional, which leads to linear matrix inequalities (LMIs). We design output-feedback point controllers in the presence of input delays using the above observer. The boundary controller is constructed using the backstepping transformation, which leads to a target system containing the exponentially decaying estimation error. The in-domain point controller is designed and analysed using an improved Wirtinger-based inequality. We show that both controllers can guarantee the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer's estimation error.

Original languageEnglish
Pages (from-to)224-233
Number of pages10
JournalAutomatica
Volume96
DOIs
StatePublished - Oct 2018

Keywords

  • Boundary control
  • Distributed parameter systems
  • Input delay
  • Networked control systems
  • Point control

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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