2021 Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System
Ghazwa F. Abd, Radhi A. Zaboon
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J. Appl. Math. 2021: 1-13 (2021). DOI: 10.1155/2021/9706255


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.


The authors would like to thank Mustansiriyah University (https://www.uomustansiriyah.edu.iq) Baghdad, Iraq, for supporting this work. The authors would also like to thank the reviewers for their thoughtful comments and efforts toward improving our manuscript.


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Ghazwa F. Abd. Radhi A. Zaboon. "Approximate Solution of a Reduced-Type Index-k Hessenberg Differential-Algebraic Control System." J. Appl. Math. 2021 1 - 13, 2021. https://doi.org/10.1155/2021/9706255


Received: 16 June 2021; Accepted: 3 September 2021; Published: 2021
First available in Project Euclid: 28 July 2021

Digital Object Identifier: 10.1155/2021/9706255

Rights: Copyright © 2021 Hindawi


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