Computational methods in optimal control : theory and practice /
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discretizations to optimal control problems. Elements...
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| Format: | Book |
| Language: | English |
| Published: |
Philadelphia :
Society for Industrial and Applied Mathematics,
[2025].
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| Series: | CBMS-NSF regional conference series in applied mathematics ;
100. |
| Subjects: |
| Summary: | Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discretizations to optimal control problems. Elements of the framework include the reference point, the truncation error, and a stability theory for the linearized first-order optimality conditions. Within this framework, the discretized control problem has a stationary point whose distance to the reference point is bounded in terms of the truncation error. The theory applies to a broad range of discretizations and provides completely new insights into the convergence theory for discrete approximations in optimal control, including the relationship between orthogonal collocation and Runge-Kutta methods. Throughout the book, derivatives associated with the discretized control problem are expressed in terms of a back-propagated costate. In particular, the objective derivative of a bang-bang or singular control problem with respect to a switch point of the control are obtained, which leads to the efficient solution of a class of nonsmooth control problems using a gradient-based optimizer. |
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| Item Description: | "This book is based on a series of ten lectures given at an NSF-CBMS conference entitled Computational Methods in Optimal Control. The conference took place between July 23 and July 27, 2018, at Jackson State University"--page xiii. |
| Physical Description: | xiii, 160 pages : illustrations (some color) ; 26 cm. |
| Bibliography: | Includes bibliographical references (pages 155-158) and index. |
| ISBN: | 9781611978254 1611978254 |