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Primer on Optimal Control TheoryPrimer on Optimal Control Theory

Jason L. Speyer and David H. Jacobson

Advances in Design and Control 20

The performance of a process — for example, how an aircraft consumes fuel — can be enhanced when the most effective controls and operating points for the process are determined. This holds true for many physical, economic, biomedical, manufacturing, and engineering processes whose behavior can often be influenced by altering certain parameters or controls to optimize some desired property or output.

Primer on Optimal Control Theory
• provides a rigorous introduction to analyzing these processes and finding the best modes of control and operation for them;

• makes optimal control theory accessible to a large class of engineers and scientists who are not mathematicians but have a basic mathematical background and need to understand the sophisticated material associated with optimal control theory;

• presents the important concepts of weak and strong control variations leading to local necessary conditions, as well as global sufficiency of Hamilton–Jacobi–Bellman theory;

• gives the second variation for local optimality where the associated Riccati equation is derived from the transition matrix of the Hamiltonian system, ideas that lead naturally to the development of H2 and H∞ synthesis algorithms.

This book will enable applied mathematicians, engineers, scientists, biomedical researchers, and economists to understand, appreciate, and implement optimal control theory at a level of sufficient generality and applicability for most practical purposes and will provide them with a sound basis from which to proceed to higher mathematical concepts and advanced systems formulations and analyses.


About the Authors
Jason L. Speyer is a Distinguished Professor in the Mechanical and Aerospace Engineering Department and the Electrical Engineering Department at the University of California, Los Angeles. Dr. Speyer has served as an Associate Editor for IEEE and AIAA journals as well as the Journal of Optimization Theory and Applications. He is a Fellow of the AIAA and a Life Fellow of the IEEE and has been honored with awards from both organizations. He is also a member of the National Academy of Engineering.

David H. Jacobson is Director of Emerging Technologies at PricewaterhouseCoopers Advisory Services, Toronto. He has held senior positions at Harvard University; University of California, Berkeley; University of the Witwatersrand, South Africa; South African Council for Scientific and Industrial Research (CSIR); Allied Electronics Corporation (Altron); and Primaxis Technology Ventures, Toronto. He is an Honorary Professor in the Department of Computational and Applied Mathematics at the University of the Witwatersrand and for 10 years served on the University’s Council. Dr. Jacobson’s published papers and books include original contributions in optimality conditions for nonlinear, constrained, and singular control systems; differential dynamic programming; and risk-sensitive decision making using exponential performance criteria.

To request an examination copy or desk copy of this book, please use our online request form at

Optimal Control, Pontryagin necessary conditions, Terminal Constaints, Global optimality, Second-order optimality

2010 / xiv + 307 pages / hardcover
ISBN: 978-0-898716-94-8 
List Price $92.00 / SIAM Member Price $64.40 / Order Code DC20
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)