Orthonormal shifted discrete Hahn polynomials for a new category of nonlinear variable‐order fractional 2D optimal control problems

The present work provides a formulation for the orthonormal shifted discrete Hahn polynomials on an arbitrary domain. We also extract some useful matrix relationshipsrelating to these discrete polynomials. These polynomials and the obtained relations are employed with the Lagrange multipliers techni...

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Bibliographic Details
Published inAsian journal of control Vol. 24; no. 4; pp. 1986 - 1997
Main Authors Heydari, Mohammad Hossein, Avazzadeh, Zakieh, Cattani, Carlo
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.07.2022
Subjects
2D optimal control problems
Boundary value problems
Caputo derivative
Lagrange multiplier
Mathematical analysis
matrix relations
Numerical methods
Optimal control
Optimization
orthonormal shifted discrete Hahn polynomials
Polynomials
Robin boundary value conditions
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Summary:The present work provides a formulation for the orthonormal shifted discrete Hahn polynomials on an arbitrary domain. We also extract some useful matrix relationshipsrelating to these discrete polynomials. These polynomials and the obtained relations are employed with the Lagrange multipliers technique to design a numerical method for solving a class of variable‐order (VO) fractional 2D optimization problems subject to Robin boundary value conditions. The proposed method converts the VO fractional system into a system of algebraic equations which readily can be solved. Some numerical examples are studied to validate and illustrate the accuracy of the introduced technique.
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.2573