Delay Compensation for Nonlienar, Adaptive, and
PDE Systems
Miroslav Krstic
Birkhauser, 2009
(to appear in October 2009)
466 pages, hardcover
ISBN-13: 978-0-8176-4698-1
CONTENTS:
Preface
1. Introduction
Part I. Linear Delay-ODE Cascades
2. Basic Predictor Feedback
3. Predictor Observers
4. Inverse Optimal Redesign
5. Robustness to Delay Mismatch
6. Time-Varying Delay
Part II. Adaptive Control
7. Delay-Adaptive Full-State Predictor Feedback
8. Delay-Adaptive Predictor with Estimation of Actuator State
9. Trajectory Tracking Under Unknown Delay and ODE Parameters
Part III. Nonlinear Systems
10. Nonlinear Predictor Feedback
11. Forward-Complete Systems
12. Strict- Feedforward Systems
13. Linearizable Strict-Feedforward Systems
Part IV. PDE-ODE Cascades
14. ODEs with General Transport-Like Actuator Dynamics
15. ODEs with Heat PDE Actuator Dynamics
16. ODEs with Wave PDE Actuator Dynamics
17. Observers for ODEs Involving PDE Sensor and Actuator Dynamics
Part V. Delay-PDE and PDE-PDE Cascades
18. Unstable Reaction-Diffusion PDE with Input Delay
19. Antistable Wave PDE with Input Delay
20. Other PDE-PDE Cascades
Appendices
References
Index
PUBLISHER'S DESCRIPTION:
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 timevarying 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 input-to-state stability,
parameter projection for adaptive control, and Bessell 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.
Written for: graduate students, researchers, and professionals in mathematics, systems
control, as well as chemical, mechanical, electrical, computer, aerospace, and
civil/structural engineering