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Optimal control theorythe variationa...

Ma, Zhongjing.

Optimal control theorythe variational method /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Optimal control theoryby Zhongjing Ma, Suli Zou.
其他題名:	the variational method /
作者:	Ma, Zhongjing.
其他作者:	Zou, Suli.
出版者:	Singapore :Springer Singapore :2021.
面頁冊數:	xix, 344 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Control theory.
電子資源:	https://doi.org/10.1007/978-981-33-6292-5
ISBN:	9789813362925$q(electronic bk.)

Optimal control theorythe variational method /
Ma, Zhongjing.

Optimal control theorythe variational method /[electronic resource] :by Zhongjing Ma, Suli Zou. - Singapore :Springer Singapore :2021. - xix, 344 p. :ill., digital ;24 cm.

Introduction -- Extrema of Functional via Variational Method -- Optimal Control via Variational Method -- Pontryagin's Minimum Principle -- Dynamic Programming -- Differential Games -- Discrete-time Optimal Control Problems.

This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin's minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin's minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.

ISBN: 9789813362925$q(electronic bk.)

Standard No.: 10.1007/978-981-33-6292-5doiSubjects--Topical Terms:

182248
Control theory.

LC Class. No.: QA402.3 / .M394 2021

Dewey Class. No.: 515.642

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505 0 $a Introduction -- Extrema of Functional via Variational Method -- Optimal Control via Variational Method -- Pontryagin's Minimum Principle -- Dynamic Programming -- Differential Games -- Discrete-time Optimal Control Problems.
520 $a This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin's minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin's minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.
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