Differential transformation and its application to nonlinear optimal control / Inseok Hwang in Transactions of the ASME . Journal of dynamic systems, measurement, and control, Vol. 131 N° 5 (Septembre 2009)  

Public ISBD [article]  inTransactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 131 N° 5 (Septembre 2009) . - 11 p. Titre : Differential transformation and its application to nonlinear optimal control Type de document : texte imprimé Auteurs : Inseok Hwang, Auteur ; Jinhua Li, Auteur ; Dzung Du, Auteur Année de publication : 2009 Article en page(s) : 11 p. Note générale : dynamic systems Langues : Anglais (eng) Mots-clés : nonlinear optimal control problems  differential transformation Résumé : 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. DEWEY : 629.8 ISSN : 0022-0434 En ligne : http://dynamicsystems.asmedigitalcollection.asme.org/Issue.aspx?issueID=26502&di [...] [article] Differential transformation and its application to nonlinear optimal control [texte imprimé] / Inseok Hwang, Auteur ; Jinhua Li, Auteur ; Dzung Du, Auteur . - 2009 . - 11 p. dynamic systems Langues : Anglais (eng) in Transactions of the ASME . Journal of dynamic systems, measurement, and control > Vol. 131 N° 5 (Septembre 2009) . - 11 p. Mots-clés : nonlinear optimal control problems  differential transformation Résumé : 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. DEWEY : 629.8 ISSN : 0022-0434 En ligne : http://dynamicsystems.asmedigitalcollection.asme.org/Issue.aspx?issueID=26502&di [...]

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