Foundations of Deterministic and Stochastic Control

1. Front Matter

   Pages i-xiv

   PDF

2. State Space Realizations

   • Jon H. Davis

   Pages 1-69

3. Least Squares Control

   • Jon H. Davis

   Pages 71-108

4. Stability Theory

   • Jon H. Davis

   Pages 109-150

5. Random Variables and Processes

   • Jon H. Davis

   Pages 151-184

6. Kalman-Bucy Filters

   • Jon H. Davis

   Pages 185-200

7. Continuous Time Models

   • Jon H. Davis

   Pages 201-228

8. The Separation Theorem

   • Jon H. Davis

   Pages 229-244

9. Luenberger Observers

   • Jon H. Davis

   Pages 245-254

10. Nonlinear and Finite State Problems

    • Jon H. Davis

    Pages 255-270

11. Wiener-Hopf Methods

    • Jon H. Davis

    Pages 271-296

12. Distributed System Regulators

    • Jon H. Davis

    Pages 297-319

13. Filters Without Riccati Equations

    • Jon H. Davis

    Pages 321-332

14. Newton’s Method for Riccati Equations

    • Jon H. Davis

    Pages 333-342

15. Numerical Spectral Factorization

    • Jon H. Davis

    Pages 343-355

16. Back Matter

    Pages 357-426

    PDF

Control theory has applications to a number of areas in engineering and communication theory. This introductory text on the subject is fairly self-contained, and consists of a wide range of topics that include realization problems, linear-quadratic optimal control, stability theory, stochastic modeling and recursive estimation algorithms in communications and control, and distributed system modeling. In the early chapters methods based on Wiener--Hopf integral equations are utilized. The fundamentals of both linear control systems as well as stochastic control are presented in a unique way so that the methods generalize to a useful class of distributed parameter and nonlinear system models. The control of distributed parameter systems (systems governed by PDEs) is based on the framework of linear quadratic Gaussian optimization problems. Additionally, the important notion of state space modeling of distributed systems is examined. Basic results due to Gohberg and Krein on convolution are given and many results are illustrated with some examples that carry throughout the text. The standard linear regulator problem is studied in the continuous and discrete time cases, followed by a discussion of (dual) filtering problems. Later chapters treat the stationary regulator and filtering problems using a Wiener--Hopf approach. This leads to spectral factorization problems and useful iterative algorithms that follow naturally from the methods employed. The interplay between time and frequency domain approaches is emphasized. "Foundations of Deterministic and Stochastic Control" is geared primarily towards advanced mathematics and engineering students in various disciplines.

• Communications
• Control/Systems Theory
• Markov model
• Markov process
• PDEs
• Stochastic processes
• Tracking
• actor
• distance
• filtering problem
• partial differential equations

"This volume is a textbook on linear control systems with an emphasis on stochastic optimal control with solution methods using spectral factorization in line with the original approach of N. Wiener. Continuous-time and discrete-time versions are presented in parallel…. Two appendices introduce functional analytic concepts and probability theory, and there are 77 references and an index. The chapters (except for the last two) end with problems…. [T]he book presents in a clear way important concepts of control theory and can be used for teaching." —Zentralblatt Math

"This is a textbook intended for use in courses on linear control and filtering and estimation on (advanced) levels. Its major purpose is an introduction to both deterministic and stochastic control and estimation. Topics are treated in both continuous time and discrete time versions…. Each chapter involves problems and exercises, and the book is supplemented by appendices, where fundamentals on Hilbert and Banach spaces, operator theory, and measure theoretic probability may be found. The book will be very useful for students, but also for a variety of specialists interested in deterministic and stochastic control and filtering." —Applications of Mathematics

"The strength of the book under review lies in the choice of specialized topics it contains, which may not be found in this form elsewhere. Also, the first half would make a good standard course in linear control." —Journal of the Indian Institute of Science

• Department of Mathematics and Statistics, Queen’s University, Kingston, Canada

  Jon H. Davis

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