Delay Compensation for Nonlinear, Adaptive, and PDE Systems

  • Miroslav Krstic

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages 1-14
  2. Miroslav Krstic
    Pages 1-13
  3. Linear Delay-ODE Cascades

    1. Front Matter
      Pages 16-16
    2. Miroslav Krstic
      Pages 17-40
    3. Miroslav Krstic
      Pages 41-52
    4. Miroslav Krstic
      Pages 53-63
    5. Miroslav Krstic
      Pages 65-83
    6. Miroslav Krstic
      Pages 85-103
  4. Adaptive Control

    1. Front Matter
      Pages 106-106
    2. Miroslav Krstic
      Pages 107-119
  5. Nonlinear Systems

    1. Front Matter
      Pages 152-152
    2. Miroslav Krstic
      Pages 153-169
    3. Miroslav Krstic
      Pages 171-190
    4. Miroslav Krstic
      Pages 191-216
    5. Miroslav Krstic
      Pages 217-231
  6. PDE-ODE Cascades

    1. Front Matter
      Pages 234-234
    2. Miroslav Krstic
      Pages 253-267
    3. Miroslav Krstic
      Pages 269-304
  7. Delay-PDE and PDE-PDE Cascades

    1. Front Matter
      Pages 330-330
    2. Miroslav Krstic
      Pages 331-355
    3. Miroslav Krstic
      Pages 357-384
    4. Miroslav Krstic
      Pages 385-391
  8. Back Matter
    Pages 1-70

About this book


Some of the most common dynamic phenomena that arise in engineering practice—actuator and sensor delays—fall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systems—the Smith predictor—has remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems.

The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay.

Specific features and topics include:

* A construction of explicit Lyapunov functionals, which can be used in control design or stability analysis, leading to a resolution of several long-standing problems in predictor feedback.

* A detailed treatment of individual classes of problems—nonlinear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time-varying delays, unknown constant delays—will help the reader master the techniques presented.

* Numerous examples ease a student new to delay systems into the topic.

* Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs.

* The basics of Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection for adaptive control, and Bessel functions are summarized in appendices for the reader’s convenience.

Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.


Boundary value problem Lyapunov functionals Lyapunov input-to-state stability Smith predictor actuator and sensor delays delay compensation for nonlinear, adaptive, PDE systems general distributed parameter systems linear delay systems linear optimization linear time-varying system linear time-varying systems state estimator and observers

Authors and affiliations

  • Miroslav Krstic
    • 1
  1. 1.Dept. Mechanical & Aerospace Engin.University of California, San DiegoLa JollaU.S.A.

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2009
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4876-3
  • Online ISBN 978-0-8176-4877-0
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • Buy this book on publisher's site
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