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 fight the harmful effects of disease? What is the most efficient way to produce a chemical substance? This book presents practical methods for solving real optimal control problems such as these.

This third edition focuses on the direct transcription method for optimal control, and features:

• A summary of relevant material in constrained optimization, including nonlinear programming.
• Discretization techniques appropriate for ordinary differential equations and differential-algebraic equations.
• Several examples and descriptions of computational algorithm formulations that implement this discretize-then-optimize strategy.
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    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.
    • More than 70 test problems and open source FORTRAN code for all of the problems.
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        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.