How do you fly an airplane from one point to another as fast as possible? What is the best way to administer a vaccine to ght the harmful e ects of disease? What is the most e cient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these. Practical Methods for Optimal Control Using Nonlinear Programming, Third Edition focuses on the direct transcription method for optimal control. It features a summary of relevant material in constrained optimization, including nonlinear programming; discretization techniques appropriate for ordinary di erential equations and di erential-algebraic equations; and several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy. The third edition has been thoroughly updated and includes new material on implicit Runge Kutta discretization techniques, new chapters on partial differential equations and delay equations, and more than 70 test problems and open source FORTRAN code for all of the problems. This book will be valuable for academic and industrial research and development in optimal control theory and applications. It is appropriate as a primary or supplementary text for advanced undergraduate and graduate students.

About the Author

John T. Betts is the author of more than 50 technical publications and two books on optimal control methods, and he remains actively engaged in research in nonlinear programming and optimal control theory. Betts retired from the Boeing Company in 2009 after serving as manager of the Operations Research Group of Boeing Computer Services (1987 1989) and as Technical Fellow in the Mathematics and Computing Technology Division, during which time he provided technical support to all areas of the company. Previously, he spent nearly two decades at The Aerospace Corporation. In 2004, he was granted an Outstanding Aerospace Engineer Award by Purdue University, and in 2011 he was named a SIAM Fellow.

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