Optimal Control

A NEW EDITION OF THE CLASSIC TEXT ON OPTIMAL CONTROL THEORY As a superb introductory text and an indispensable reference, this new edition of Optimal Control will serve the needs of both the professional engineer and the advanced student in mechanical, electrical, and aerospace engineering. Its coverage encompasses all the fundamental topics as well as the major changes that have occurred in recent years. An abundance of computer simulations using MATLAB and relevant Toolboxes is included to give the reader the actual experience of applying the theory to real-world situations. Major topics covered include: Static Optimization Optimal Control of Discrete-Time Systems Optimal Control of Continuous-Time Systems The Tracking Problem and Other LQR Extensions Final-Time-Free and Constrained Input Control Dynamic Programming Optimal Control for Polynomial Systems Output Feedback and Structured Control Robustness and Multivariable Frequency-Domain Techniques Differential Games Reinforcement Learning and Optimal Adaptive Control

A focused presentation of how sparse optimization methods can be used to solve optimal control and estimation problems.

In the late 1950's, the group of Soviet mathematicians consisting of L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko made fundamental contributions to optimal control theory. Much of their work was collected in their monograph, The Mathematical Theory of Optimal Processes. Subsequently, Professor Gamkrelidze made further important contributions to the theory of necessary conditions for problems of optimal control and general optimization problems. In the present monograph, Professor Gamkrelidze presents his current view of the fundamentals of optimal control theory. It is intended for use in a one-semester graduate course or advanced undergraduate course. We are now making these ideas available in English to all those interested in optimal control theory. West Lafayette, Indiana, USA Leonard D. Berkovitz Translation Editor Vll Preface This book is based on lectures I gave at the Tbilisi State University during the fall of 1974. It contains, in essence, the principles of general control theory and proofs of the maximum principle and basic existence theorems of optimal control theory. Although the proofs of the basic theorems presented here are far from being the shortest, I think they are fully justified from the conceptual view point. In any case, the notions we introduce and the methods developed have one unquestionable advantage -they are constantly used throughout control theory, and not only for the proofs of the theorems presented in this book.

Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.

Geared toward advanced undergraduate and graduate engineering students, this text introduces the theory and applications of optimal control. It serves as a bridge to the technical literature, enabling students to evaluate the implications of theoretical control work, and to judge the merits of papers on the subject. Rather than presenting an exhaustive treatise, Optimal Control offers a detailed introduction that fosters careful thinking and disciplined intuition. It develops the basic mathematical background, with a coherent formulation of the control problem and discussions of the necessary conditions for optimality based on the maximum principle of Pontryagin. In-depth examinations cover applications of the theory to minimum time, minimum fuel, and to quadratic criteria problems. The structure, properties, and engineering realizations of several optimal feedback control systems also receive attention. Special features include numerous specific problems, carried through to engineering realization in block diagram form. The text treats almost all current examples of control problems that permit analytic solutions, and its unified approach makes frequent use of geometric ideas to encourage students' intuition.

From the reviews: "The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. . . .In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-to-read fashion." —Measurement and Control

“Each chapter contains a well-written introduction and notes. They include the author's deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control." —Mathematical Reviews “Thanks to a great effort to be self-contained, [this book] renders accessibly the subject to a wide audience. Therefore, it is recommended to all researchers and professionals interested in Optimal Control and its engineering and economic applications. It can serve as an excellent textbook for graduate courses in Optimal Control (with special emphasis on Nonsmooth Analysis)." —Automatica

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control