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Numerical solution for classical optimal control problem governing by hyperbolic partial differential equation via galerkin finite element-implicit method with gradient projection method
Joint Authors
al-Rawdani, Iman H.
al-Hawasy, Jamil A. Ali
Source
Ibn al-Haitham Journal for Pure and Applied Science
Issue
Vol. 32, Issue 2 (31 Aug. 2019), pp.71-80, 10 p.
Publisher
University of Baghdad College of Education for Pure Science / Ibn al-Haitham
Publication Date
2019-08-31
Country of Publication
Iraq
No. of Pages
10
Main Subjects
Topics
Abstract EN
This paper deals with the numerical solution of the discrete classical optimal control problem (DCOCP) governing by linear hyperbolic boundary value problem (LHBVP).
The method which is used here consists of: the GFEIM " the Galerkin finite element method in space variable with the implicit finite difference method in time variable" to find the solution of the discrete state equation (DSE) and the solution of its corresponding discrete adjoint equation, where a discrete classical control (DCC) is given.
The gradient projection method with either the Armijo method (GPARM) or with the optimal method (GPOSM) is used to solve the minimization problem which is obtained from the necessary condition for optimality of the DCOCP to find the DCC .An algorithm is given and a computer program is coded using the above methods to find the numerical solution of the DCOCP with step length of space variable h = 0.1, and step length of time variable At = 0.05.
Illustration examples are given to explain the efficiency of these methods.
The results show the methods which are used here are better than those obtained when we used the Gradient method (GM) or Frank Wolfe method (FWM) with Armijo step search method to solve the minimization problem.
American Psychological Association (APA)
al-Hawasy, Jamil A. Ali& al-Rawdani, Iman H.. 2019. Numerical solution for classical optimal control problem governing by hyperbolic partial differential equation via galerkin finite element-implicit method with gradient projection method. Ibn al-Haitham Journal for Pure and Applied Science،Vol. 32, no. 2, pp.71-80.
https://search.emarefa.net/detail/BIM-899797
Modern Language Association (MLA)
al-Hawasy, Jamil A. Ali& al-Rawdani, Iman H.. Numerical solution for classical optimal control problem governing by hyperbolic partial differential equation via galerkin finite element-implicit method with gradient projection method. Ibn al-Haitham Journal for Pure and Applied Science Vol. 32, no. 2 (Aug. 2019), pp.71-80.
https://search.emarefa.net/detail/BIM-899797
American Medical Association (AMA)
al-Hawasy, Jamil A. Ali& al-Rawdani, Iman H.. Numerical solution for classical optimal control problem governing by hyperbolic partial differential equation via galerkin finite element-implicit method with gradient projection method. Ibn al-Haitham Journal for Pure and Applied Science. 2019. Vol. 32, no. 2, pp.71-80.
https://search.emarefa.net/detail/BIM-899797
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 79-80
Record ID
BIM-899797