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A new high accurate approximate approach to solve optimal control problems of fractional order via efficient basis functions
- Source :
- Alexandria Engineering Journal, Vol 61, Iss 8, Pp 5805-5818 (2022)
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- Investigation of spectral (collocation or Galerkin) methods for the solution approximation of different classes of optimal control problems have had been increased in recent years. In this research work, we proposed and analyzed an applicable Legendre spectral collocation approach, based on an efficient space of fractional basis functions, to compute numerically the solution of fractional optimal control problems. We first introduce a fractional Lagrange interpolation and then approximate the unknown control and state by this new set of fractional interpolation functions. The problem is discretized in terms of shifted Legendre–Gauss collocation points and two approaches are suggested to calculate the exact fractional differentiation matrix. Also, we prove that the approximate solutions of the obtained discretized problem converge to the optimal solution of the main problem by assuming some mild conditions. The method is implemented for three numerical test problems to show the claimed efficiency and capability.
- Subjects :
- Collocation
Discretization
Analysis of convergence
MathematicsofComputing_NUMERICALANALYSIS
General Engineering
Lagrange polynomial
Basis function
Nonlinear programming problems
Engineering (General). Civil engineering (General)
Optimal control
symbols.namesake
symbols
Applied mathematics
TA1-2040
Galerkin method
Legendre polynomials
Fractional optimal control problems
Lagrange interpolation of fractional order
Mathematics
Interpolation
Subjects
Details
- ISSN :
- 11100168
- Volume :
- 61
- Database :
- OpenAIRE
- Journal :
- Alexandria Engineering Journal
- Accession number :
- edsair.doi.dedup.....8694061f14e2b5c0ae98335ad618c7a1