Optimal control : an introduction to the theory with applications
著者
書誌事項
Optimal control : an introduction to the theory with applications
（Oxford applied mathematics and computing science series）
Clarendon Press, 1991
- : pbk
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注記
Including bibliographical reference and index
内容説明・目次
- 巻冊次
-
ISBN 9780198596752
内容説明
Systems that evolve with time occur frequently in nature and modelling the behaviour of such systems provides an important application of mathematics. These systems can be completely deterministic, but it may be possible too to control their behaviour by intervention through "controls". The theory of optimal control is concerned with determining such controls which, at minimum cost, either direct the system along a given trajectory or enable it to reach a given point in its state space. This textbook is a straightforward introduction to the theory of optimal control with an emphasis on presenting many different applications. Professor Hocking has taken pains to ensure that the theory is developed to display the main themes of the arguments but without using sophisticated mathematical tools. Problems in this setting can arise across a wide range of subjects and there are illustrative examples of systems from as diverse fields as dynamics, economics, population control, and medicine. Throughout there are many worked examples, and numerous exercises (with solutions) are provided.
目次
- Optimal control problems
- Systems of differential equations, matrices, and sets
- Part A Time-Optimal Control of Linear Systems: Controllability
- Time-optimal control
- Further examples
- Part B The Pontryagin Maximum Principle: The basic Pontryagin Maximum Principle (PMP)
- Extensions to the PMP
- Linear state equations with quadratic costs
- Proof of the Pontryagin Maximum Principle
- Further applications and extensions
- Part C Applications of Optimal Control Theory: Some applied optimal control problems
- Numerical methods for optimal control problems outline solutions to the exercises.
- 巻冊次
-
: pbk ISBN 9780198596820
内容説明
Systems that evolve with time occur frequently in nature and modelling the behaviour of such systems provides an important application of mathematics. These systems can be completely deterministic, but it may be possible too to control their behaviour by intervention through 'controls'. The theory of optimal control is concerned with determining such controls which, at minimum cost, either direct the system along a given trajectory or enable it to reach a given point
in its state space.
This textbook is a straightforward introduction to the theory of optimal control with an emphasis on presenting many different applications. Professor Hocking has taken pains to ensure that the theory is developed to display the main themes of the arguments but without using sophisticated mathematical tools.
Problems in this setting can arise across a wide range of subjects and there are illustrative examples of systems from as diverse fields as dynamics, economics, population control, and medicine. Throughout there are many worked examples, and numerous exercises (with solutions) are provided.
目次
- Optimal control problems
- Systems of differential equations, matrices, and sets
- Part A Time-Optimal Control of Linear Systems: Controllability
- Time-optimal control
- Further examples
- Part B The Pontryagin Maximum Principle: The basic Pontryagin Maximum Principle (PMP)
- Extensions to the PMP
- Linear state equations with quadratic costs
- Proof of the Pontryagin Maximum Principle
- Further applications and extensions
- Part C Applications of Optimal Control Theory: Some applied optimal control problems
- Numerical methods for optimal control problems
- Bibliography
- Outline solutions to the exercises
- Index
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