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Preface It is my pleasure to present this book on optimal control geared toward chemical engineers. The application of optimal control is a logical step when it comes to pushing the envelopes of unit operations and processes undergoing changes with time and space. This book is essentially a summary of important concepts I have learned in the last 16 years from the classroom, self-study, and research along with interaction with some great individuals including teachers, authors, peers, and students.
The goal of this book is to provide a sufficiently detailed treatment of optimal control that will enable readers to formulate optimal control problems and solve them. With this emphasis, the book provides necessary mathematical analyses and derivations of important results. It is assumed that the reader is at the level of a graduate student. Chapter 1 stimulates interest in optimal control by describing various processes and introducing the mathematical description of optimal control problems. Against this backdrop, readers are introduced to the basic concepts of optimal control in Chapter 2. The notion of optimality is presented and analyzed in Chapter 3. The ubiquitous Lagrange multipliers are introduced in this chapter.
They are elaborated later in Chapter 4 along with important theorems and rules of application. Chapter 5 presents the celebrated Pontryagin’s principle of optimal control. With this background, Chapter 6 puts together different types of optimal control problems and the necessary conditions for optimality. Chapter 7 describes important numerical methods and computational algorithms in a lucid manner to solve a wide range of optimal control problems.
Chapter 8 introduces the optimal control of processes that are periodic and provides relevant numerical methods and algorithms. A brief review of mathematical concepts is provided in Chapter 9. Chapter-end bibliographies contain the cited references as well as important sources on which I have relied. For an introductory one-semester course, instructors can consider Chapters 1–3, the main results from Chapters 4 and 5, and Chapters 6 and 7. An advanced course may include all chapters with obviously less time devoted to the first three. Chapters 7 and 8 may form a part of an advanced optimization course. Containing all relevant mathematical results and their derivations, the book encourages self-study.
During initial readings, some readers might want to skip a derivation, accept the result temporarily, and focus more on the applications. A working knowledge of computer programming is highly recommended to solve optimal control problems — whether one intends to write one’s own programs or use software and programs developed by others. Optimal control is the result of tremendous contributions of wonderful mathematicians, scientists, and engineers. To list their achievements is a formidable task. What I have presented in this book is what I could understand and have first-hand experience with. I hope the savants will help me in improving this book and the students will find the book useful.
I am profoundly grateful to Dr. Anil Mehrotra, Dr. Ayodeji Jeje, and Dr. Robert Heidemann for their assiduous mentoring and training during my doctorate and postdoctoral fellowship at the University of Calgary. I am thankful to my graduate students, especially Amir Sani, Hameed Muhamad, Dinesh Kumar Patel, and Vishalkumar Patel for helping with the proofreading. I acknowledge Allison Shatkin, Karen Simon, and Marsha Pronin at CRC Press who have offered superb assistance in the writing of this book. I am very appreciative of the outstanding contributions of the developers of TEX, LATEX, MiKTEX, Xfig, Asymptote, AUCTEX, and GNU Emacs — the primary applications I have used to prepare the book