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    Differential Transformation and Its Application to Nonlinear Optimal Control

    Source: Journal of Dynamic Systems, Measurement, and Control:;2009:;volume( 131 ):;issue: 005::page 51010
    Author:
    Inseok Hwang
    ,
    Jinhua Li
    ,
    Dzung Du
    DOI: 10.1115/1.3155013
    Publisher: The American Society of Mechanical Engineers (ASME)
    Abstract: A novel numerical method based on the differential transformation is proposed for solving nonlinear optimal control problems in this paper. The differential transformation is a linear operator that transforms a function from the original time and/or space domain into another domain in order to simplify the differential calculations. The optimality conditions for the optimal control problems can be represented by algebraic and differential equations. Using the differential transformation, these algebraic and differential equations with their boundary conditions are first converted into a system of nonlinear algebraic equations. Then the numerical optimal solutions are obtained in the form of finite-term Taylor series by solving the system of nonlinear algebraic equations. The differential transformation algorithm is similar to the spectral element methods in that the computational region splits into several subregions but it uses polynomials of high degrees by keeping a small number of subregions. The differential transformation algorithm could solve the finite- (or infinite-) time horizon optimal control problems formulated as either the algebraic and ordinary differential equations using Pontryagin’s minimum principle or the Hamilton–Jacobi–Bellman partial differential equation using dynamic programming in one unified framework. In addition, the differential transformation algorithm can efficiently solve optimal control problems with the piecewise continuous dynamics and/or nonsmooth control. The performance is demonstrated through illustrative examples.
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      Differential Transformation and Its Application to Nonlinear Optimal Control

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    http://yetl.yabesh.ir/yetl1/handle/yetl/140183
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    contributor authorInseok Hwang
    contributor authorJinhua Li
    contributor authorDzung Du
    date accessioned2017-05-09T00:32:08Z
    date available2017-05-09T00:32:08Z
    date copyrightSeptember, 2009
    date issued2009
    identifier issn0022-0434
    identifier otherJDSMAA-26502#051010_1.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/140183
    description abstractA novel numerical method based on the differential transformation is proposed for solving nonlinear optimal control problems in this paper. The differential transformation is a linear operator that transforms a function from the original time and/or space domain into another domain in order to simplify the differential calculations. The optimality conditions for the optimal control problems can be represented by algebraic and differential equations. Using the differential transformation, these algebraic and differential equations with their boundary conditions are first converted into a system of nonlinear algebraic equations. Then the numerical optimal solutions are obtained in the form of finite-term Taylor series by solving the system of nonlinear algebraic equations. The differential transformation algorithm is similar to the spectral element methods in that the computational region splits into several subregions but it uses polynomials of high degrees by keeping a small number of subregions. The differential transformation algorithm could solve the finite- (or infinite-) time horizon optimal control problems formulated as either the algebraic and ordinary differential equations using Pontryagin’s minimum principle or the Hamilton–Jacobi–Bellman partial differential equation using dynamic programming in one unified framework. In addition, the differential transformation algorithm can efficiently solve optimal control problems with the piecewise continuous dynamics and/or nonsmooth control. The performance is demonstrated through illustrative examples.
    publisherThe American Society of Mechanical Engineers (ASME)
    titleDifferential Transformation and Its Application to Nonlinear Optimal Control
    typeJournal Paper
    journal volume131
    journal issue5
    journal titleJournal of Dynamic Systems, Measurement, and Control
    identifier doi10.1115/1.3155013
    journal fristpage51010
    identifier eissn1528-9028
    treeJournal of Dynamic Systems, Measurement, and Control:;2009:;volume( 131 ):;issue: 005
    contenttypeFulltext
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    DSpace software copyright © 2002-2015  DuraSpace
    نرم افزار کتابخانه دیجیتال "دی اسپیس" فارسی شده توسط یابش برای کتابخانه های ایرانی | تماس با یابش
    yabeshDSpacePersian