"An excellent introduction to optimal control and estimation theory and its relationship with LQG design .... invaluable as a reference for those already familiar with the subject." -This highly regarded graduate-level text provides a comprehensive introduction to optimal control theory for stochastic systems, emphasizing application of its basic concepts to real problems.Automatica

*Optimal Control and Estimation* is organized in six chapters and an epilogue.

__Introduction__(Chapter 1) Overview of goals for optimal control and modeling of dynamic systems.__The Mathematics of Control and Estimation__(Chapter 2) Each section presents the mathematical concepts used in each chapter of the book. Section 2.1 reviews the basics of scalars, vectors, and matrices. Section 2.2 reviews matrix properties and operations. Section 2.3 presents dynamic models and solutions. Section 2.4 discusses random variables, sequences, and processes. Section 2.5 addresses properties of dynamic systems. Section 2.6 deals with frequency domain modeling and analysis.__Optimal Trajectories and Neighboring-Optimal Solutions__(Chapter 3) Cost functions, parametric optimization, conditions for optimality, constraints and singular control, numerical optimization, and neighboring-optimal solutions are presented.__Optimal State Estimation__(Chapter 4) The chapter addresses least-squares estimation, propagation of the state estimate and uncertainty, discrete-time optimal filters and predictors, correlated disturbance inputs and measurements, continuous-time optimal filters and predictors, optimal nonlinear estimation, and adaptive filtering.__Stochastic Optimal Control__(Chapter 5) Optimization of nonlinear systems with random inputs, perfect inputs, and imperfect inputs are described. Certainty-equivalance and the separation property are presented for continuous- and discrete-time systems.__Linear Multivariable Control__(Chapter 6) Solution of the algebraic Riccati equation, steady-state response to commands, modal properties of optimal control systems, and robustness of linear-quadratic regulators and stochastic-optimal regulators are presented.- The
__Epilogue__briefly discusses the implications of the book."An excellent teaching book with many examples and worked problems that would be ideal for self study or for use in the classroom .... The book also has a practical orientation and would be of considerable use to people applying these techniques in practice." -

*Short Book Reviews, Publication of the International Statistical Institute*"An excellent book which guides the reader through most of the important concepts and techniques of the title subject .... A useful book for students (and their teachers) and for those practising engineers who require a comprehensive reference to the subject." -

Unabridged, corrected Dover (1994) republication of*Library Reviews, The Royal Aeronautical Society**Stochastic Optimal Control: Theory and Application*, published by John Wiley & Sons, New York, 1986. 142 illustrations. Preface to Dover edition. Biography of author. Problems. References. Index. xv + 639 pp. 5-5/8 x 8-1/4. Paperbound. ISBN 0-486-68200-5.### Additional review comments:

"The book provides an excellent introductory text to the broad field of optimization .... The highly readable text is complemented with both examples and references enabling the reader to research further points of particular interest." -

*Automatica*"A valuable book which provides an illuminating insight into many aspects of optimal control .... the reader finds the concepts and methodology expounded in a progressive direct manner, marked by clarity of insight and presentation .... This lucidly written book by Stengel can be confidently recommended to anyone desiring to develop a thorough working knowledge of the subject of stochastic optimal control. It should certainly find a place in the reference library." -

*Robotica*"... describes a body of techniques that is quite useful in determining the best strategy for controlling a system in the presence of uncertainty.... The power of stochastic optimal control becomes apparent, as interpreted by notions drawn from classical control applied to multi-input/multi-output systems .... Although many interesting developments in control system analysis have been made recently, optimality remains the most important unifying criterion for control system synthesis." -

*IEEE Control Systems Magazine*"This book is a great one for people interested in nonlinear controls and the Kalman filter at a budget cost. The book introduces stochastic optimal control concepts for application to actual problems with sufficient theoretical background to justify their use, but not enough to get bogged down in the math. The book gives the reader with little background in control theory the tools to design practical control systems and the confidence to tackle more advanced literature - something that both the professional who is a little rusty and the student can appreciate.... There are also numerous worked out numerical examples, which is a welcome pleasure in such books that are often very theoretical. Highly recommended." -

*Anon (2008), Amazon*"Great book, I'm toward the end of my PhD, really wish I had come across this book sooner, very well done, presented in down to earth manner." -

*Anon (2018), Amazon*"This is a very well written book. A lot of good info in here with interesting examples of how to apply the content. Most of the optimal control books that I have seen are impossible to understand unless you are a mathematician, but this one is different. This is a great book for engineers." -

*Anon (2015), Amazon*#### Dover Press Listing

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**Robert F. Stengel**is Professor Emeritus and former Associate Dean of Engineering and Applied Science at Princeton University. He is the author of(Princeton University Press, 2022). He was principal designer of the Apollo Lunar Module manual attitude control logic.**Flight Dynamics, Second Edition**#### Errata

- p. 56: Remove the following sentence: "As an exercise, verify that the same result would have been computed with the unweighted pseudoinverse and A= (1/10 1/20 1/30)." (KMcD, 2014)
- p.76, eq. 2.3-38: Order of coefficients in third row is reversed. Should be [c1 c2 c3]. (CY, 2020)
- p. 147, eq. 2.5-131: Change "ds" to "dt". (RFS, 2012)
- p. 276, eq. 3.7-29: Change "... M^T)P^T" to "... M^T)^T P". (RWB, 2009)
- p. 282, eq. 3.7-59: Second line of equation; change "delta-u-sub-k" to "(delta-u-sub-k)^T". (RFS, 2012)
- p. 392, eq. 4.6-61: Change E[f(x)] to E[h(x)]. (VS, 2017)
- p. 481, eq. 5.4-59a: The matrix [L 0; L K] should be [L 0; L -K]. (SH, 2012)
- p. 524, eq. 6.3-41: Change "chi(t)" to "chi^T(t)". (RWB, 2009)
- p. 596. eq. 6.5-82: Change "sigma on ..." to "s on ...". (RWB, 2009)

**http://www.stengel.mycpanel.princeton.edu/OptConEst.html**

__key words__: optimization, optimal control, probability theory, statistics, optimal state estimation, Kalman filter, control systems, multivariable control, nonlinear control, adaptive control, robustness.

Last updated on November 6, 2022.

Copyright 2022 by Robert F. Stengel. All rights reserved.