Distributed nonlinear control of diffusion-reaction processes

Stevan Dubljevic, Panagiotis D. Christofides, Ioannis G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


In this work, we focus on distributed control of quasi-linear parabolic partial differential equations (PDEs) and address the problem of enforcing a prespecified spatio-temporal behaviour in the closed-loop system using nonlinear feedback control and a sufficiently large number of actuators and sensors. Under the assumption that the desired spatio-temporal behaviour is described by a 'target parabolic PDE', we use a combination of Galerkin's method and nonlinear control techniques to design nonlinear state and static output feedback controllers to address this problem. We use examples of diffusion-reaction processes to demonstrate the formulation of the control problem and the effectiveness of our systematic approach to creating prespecified spatio-temporal behaviour. Using these illustrative examples, we demonstrate that both (a) a sufficiently large number of actuators/sensors, and (b) nonlinear control laws are needed to achieve this goal.

Original languageEnglish (US)
Pages (from-to)133-156
Number of pages24
JournalInternational Journal of Robust and Nonlinear Control
Issue number2
StatePublished - Jan 24 2004

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Aerospace Engineering
  • General Chemical Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Industrial and Manufacturing Engineering
  • Biomedical Engineering


  • Diffusion-reaction processes
  • Distributed parameter systems
  • Galerkin's method
  • Nonlinear control
  • Target parabolic PDE


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