Computational Methods Optimal Control by William Hager (17 results)
Language: English
Published by MP-SIA SIAM - Society for Industrial and Applied M, 2025
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Paperback. Condition: New. 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 discrete approximations to optimal control problems. Elem…ents 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.
Language: English
Published by SIAM - Society for Industrial and Applied Mathematics, 2025
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Language: English
Published by SIAM - Society for Industrial and Applied Mathematics, 2025
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Language: English
Published by SIAM - Society for Industrial and Applied Mathematics, 2025
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Published by Society for Industrial & Applied Mathematics,U.S., 2025
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Language: English
Published by MPSIA SIAM Society for Industrial and Applied M, 2025
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Language: English
Published by SIAM - Society for Industrial and Applied Mathematics, 2025
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Published by SIAM - Society for Industrial and Applied Mathematics, 2025
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Language: English
Published by Society for Industrial & Applied Mathematics,U.S., New York, 2025
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Paperback. Condition: new. Paperback. 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 discrete approximations to optimal control pro…blems. 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 RungeKutta 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. Unifying rigorous theory and numerical insights, this framework assesses convergence in discrete optimal control via truncation error bounds and stability analysis. It uncovers links between collocation, Runge-Kutta methods, and gradient-based strategies for tackling nonsmooth challenges. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
Language: English
Published by SIAM - Society for Industrial and Applied Mathematics, 2025
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Published by Society for Industrial & Applied Mathematics,U.S., 2025
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Language: English
Published by Society for Industrial & Applied Mathematics,U.S., 2025
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Language: English
Published by Society for Industrial & Applied Mathematics,U.S., New York, 2025
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Paperback. Condition: new. Paperback. 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 discrete approximations to optimal control pro…blems. 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 RungeKutta 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. Unifying rigorous theory and numerical insights, this framework assesses convergence in discrete optimal control via truncation error bounds and stability analysis. It uncovers links between collocation, Runge-Kutta methods, and gradient-based strategies for tackling nonsmooth challenges. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
Language: English
Published by Society for Industrial and Applied Mathematics,U.S., US, 2025
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Paperback. Condition: New. 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 discrete approximations to optimal control problems. Elem…ents 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.
Language: English
Published by Society for Industrial & Applied Mathematics,U.S., New York, 2025
- Softcover
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Paperback. Condition: new. Paperback. 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 discrete approximations to optimal control pro…blems. 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 RungeKutta 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. Unifying rigorous theory and numerical insights, this framework assesses convergence in discrete optimal control via truncation error bounds and stability analysis. It uncovers links between collocation, Runge-Kutta methods, and gradient-based strategies for tackling nonsmooth challenges. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
Language: English
Published by SIAM - Society for Industrial and Applied Mathematics, 2025
- Softcover
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