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Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint
Author(s) -
Ashpazzadeh Elmira,
Lakestani Mehrdad,
Yildirim Ahmet
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2615
Subject(s) - biorthogonal system , mathematics , fractional calculus , constraint (computer aided design) , fractional programming , operator (biology) , nonlinear system , optimal control , mathematical optimization , nonlinear programming , computer science , wavelet , wavelet transform , biochemistry , chemistry , physics , geometry , repressor , quantum mechanics , artificial intelligence , transcription factor , gene
Summary This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann‐Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well‐developed algorithms may be applied. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The method is computationally very attractive and gives very accurate results.