Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System
This study focuses on developing an efficient and easily implemented novel technique to solve the index-k Hessenberg differential-algebraic equation (DAE) with input control. The implicit function theorem is first applied to solve the algebraic constraints of having unknown state differential variab...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9706255 |
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| author | Ghazwa F. Abd Radhi A. Zaboon |
| author_facet | Ghazwa F. Abd Radhi A. Zaboon |
| author_sort | Ghazwa F. Abd |
| collection | DOAJ |
| description | This study focuses on developing an efficient and easily implemented novel technique to solve the index-k Hessenberg differential-algebraic equation (DAE) with input control. The implicit function theorem is first applied to solve the algebraic constraints of having unknown state differential variables to form a reduced state-space representation of an ordinary differential (control) system defined on smooth manifold with consistent initial conditions. The variational formulation is then developed for the reduced problem. A solution of the reduced problem is proven to be the critical point of the variational formulation, and the critical points of the variational formulation are the solutions of the reduced problem on the manifold. The approximate analytical solution of the equivalent variational formulation is represented as a finite number of basis functions with unknown parameters on a suitable separable Hilbert setting solution space. The unknown coefficients of the solution are obtained by solving a linear algebraic system. The different index problems of linear Hessenberg differential-algebraic control systems are approximately solved using this approach with comparisons. The numerical results reveal the good efficiency and accuracy of the proposed method. This technique is applicable for a large number of applications like linear quadratic optima, control problems, and constrained mechanical systems. |
| format | Article |
| id | doaj-art-f278775a689d403aa9ab2bf143a7db14 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-f278775a689d403aa9ab2bf143a7db142025-02-03T01:25:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/97062559706255Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control SystemGhazwa F. Abd0Radhi A. Zaboon1Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, IraqDepartment of Mathematics, College of Science, Mustansiriyah University, Baghdad, IraqThis study focuses on developing an efficient and easily implemented novel technique to solve the index-k Hessenberg differential-algebraic equation (DAE) with input control. The implicit function theorem is first applied to solve the algebraic constraints of having unknown state differential variables to form a reduced state-space representation of an ordinary differential (control) system defined on smooth manifold with consistent initial conditions. The variational formulation is then developed for the reduced problem. A solution of the reduced problem is proven to be the critical point of the variational formulation, and the critical points of the variational formulation are the solutions of the reduced problem on the manifold. The approximate analytical solution of the equivalent variational formulation is represented as a finite number of basis functions with unknown parameters on a suitable separable Hilbert setting solution space. The unknown coefficients of the solution are obtained by solving a linear algebraic system. The different index problems of linear Hessenberg differential-algebraic control systems are approximately solved using this approach with comparisons. The numerical results reveal the good efficiency and accuracy of the proposed method. This technique is applicable for a large number of applications like linear quadratic optima, control problems, and constrained mechanical systems.http://dx.doi.org/10.1155/2021/9706255 |
| spellingShingle | Ghazwa F. Abd Radhi A. Zaboon Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System Journal of Applied Mathematics |
| title | Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System |
| title_full | Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System |
| title_fullStr | Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System |
| title_full_unstemmed | Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System |
| title_short | Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System |
| title_sort | approximate solution of a reduced type index k hessenberg differential algebraic control system |
| url | http://dx.doi.org/10.1155/2021/9706255 |
| work_keys_str_mv | AT ghazwafabd approximatesolutionofareducedtypeindexkhessenbergdifferentialalgebraiccontrolsystem AT radhiazaboon approximatesolutionofareducedtypeindexkhessenbergdifferentialalgebraiccontrolsystem |