Robust control of hyperbolic PDE systems

Panagiotis D. Christofides, Prodromos Daoutidis

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104 Scopus citations


This work concerns systems of quasi-linear first-order hyperbolic partial differential equations (PDEs) with uncertain variables and unmodeled dynamics. For systems with uncertain variables, the problem of complete elimination of the effect of uncertainty on the output via distributed feedback (uncertainty decoupling) is initially considered; a necessary and sufficient condition for its solvability as well as explicit controller synthesis formulas are derived. Then, the problem of synthesizing a distributed robust controller that achieves asymptotic output tracking with arbitrary degree of attenuation of the effect of uncertain variables on the output of the closed-loop system is addressed and solved. Robustness with respect to unmodeled dynamics is studied within a singular perturbation framework. It is established that controllers which are synthesized on the basis of a reduced-order slow model, and achieve uncertainty decoupling or uncertainty attenuation, continue to enforce these objectives in the presence of unmodeled dynamics, provided that they are stable and sufficiently fast. The developed controller synthesis results are successfully implemented through simulations on a fixed-bed reactor, modeled by two quasi-linear first-order hyperbolic PDEs, where the reactant wave propagates through the bed with significantly larger speed than the heat wave, and the heat of reaction is unknown and time varying.

Original languageEnglish (US)
Pages (from-to)85-105
Number of pages21
JournalChemical Engineering Science
Issue number1
StatePublished - Jan 1998

Bibliographical note

Funding Information:
This work was supported by the Office of Industrial Technology, Advanced Industrial Concepts Division of the U.S. Department of Energy under contract DE-AC03-76SF00098 and the San Diego Supercomputer Center. B. L. T. acknowledges support from a National Sciences Foundation Graduate Fellowship award and A. K. C. acknowledges support from a National Science Foundation National Young Investigator Award and the Camille and Henry Dreyfus Foundation.


  • Convection-reaction processes
  • Lyapunov's direct method
  • Uncertain systems


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