Open AccessCaputo fractional derivative operational matrices of Legendre and Chebyshev wavelets in fractional delay optimal control
Author(s) -
Iman Malmir
Publication year - 2022
Publication title -
numerical algebra, control and optimization
Language(s) - English
Resource type - Journals
eISSN - 2155-3289
pISSN - 2155-3297
DOI - 10.3934/naco.2021013
Subject(s) - legendre wavelet , chebyshev filter , legendre polynomials , fractional calculus , mathematics , wavelet , optimal control , quadratic equation , mathematical optimization , mathematical analysis , computer science , wavelet transform , discrete wavelet transform , geometry , artificial intelligence
Caputo derivative operational matrices of the arbitrary scaled Legendre and Chebyshev wavelets are introduced by deriving directly from these wavelets. The Caputo derivative operational matrices are used in quadratic optimization of systems having fractional or integer orders differential equations. Using these operational matrices, a new quadratic programming wavelet-based method without doing any integration operation for finding solutions of quadratic optimal control of traditional linear/nonlinear fractional time-delay constrained/unconstrained systems is introduced. General strategies for handling different types of the optimal control problems are proposed.