Finite-dimensional observer-based controller for linear 1-D heat equation: An LMI approach

R. Katz*, E. Fridman

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

The objective of the present paper is finite-dimensional observer-based control of 1-D linear heat equation with constructive and easily implementable design conditions. We propose a modal decomposition approach in the cases of bounded observation and control operators (i.e, non-local sensing and actuation). The dimension of the controller is equal to the number of modes which decay slower than a given decay rate δ > 0. The observer may have a larger dimension N. The observer and controller gains are found separately of each other. We suggest a direct Lyapunov approach to the full-order closed-loop system and provide linear matrix inequalities (LMIs) for finding N and the exponential decay rate of the closed-loop system. Different from some existing qualitative methods, we prove that the LMIs are always feasible for large enough N leading to easily verifiable conditions. A numerical example demonstrates the efficiency of our method that gives non-conservative bounds on N and δ.

Original languageEnglish
Pages (from-to)7611-7616
Number of pages6
JournalIFAC-PapersOnLine
Volume53
Issue number2
DOIs
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: 12 Jul 202017 Jul 2020

Keywords

  • Distributed parameter systems
  • Heat equation
  • Lyapunov method
  • Modal decomposition
  • Observer-based control

Fingerprint

Dive into the research topics of 'Finite-dimensional observer-based controller for linear 1-D heat equation: An LMI approach'. Together they form a unique fingerprint.

Cite this