Biorthogonal cubic Hermite spline multiwavelets on the interval for solving the fractional optimal control problems
Authors
Abstract:
In this paper, a new numerical method for solving fractional optimal control problems (FOCPs) is presented. The fractional derivative in the dynamic system is described in the Caputo sense. The method is based upon biorthogonal cubic Hermite spline multiwavelets approximations. The properties of biorthogonal multiwavelets are first given. The operational matrix of fractional Riemann-Lioville integration and multiplication are then utilized to reduce the given optimization problem to the system of algebraic equations. In order to save memory requirement and computational time, a threshold procedure is applied to obtain algebraic equations. Illustrative examples are provided to confirm the applicability of the new method.
similar resources
biorthogonal cubic hermite spline multiwavelets on the interval for solving the fractional optimal control problems
in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...
full textBiorthogonal Multiwavelets on the Interval: Cubic Hermite Splines
Starting with Hermite cubic splines as the primal multigenerator, first a dual multigenerator onR is constructed that consists of continuous functions, has small support, and is exact of order 2. We then derive multiresolution sequences on the interval while retaining the polynomial exactness on the primal and dual sides. This guarantees moment conditions of the corresponding wavelets. The conc...
full textBiorthogonal cubic Hermite spline multiwavelets on the interval with complementary boundary conditions
In this article, a new biorthogonal multiwavelet basis on the interval with complementary homogeneous Dirichlet boundary conditions of second order is presented. This construction is based on the multiresolution analysis onR introduced in [DHJK00] which consists of cubic Hermite splines on the primal side. Numerical results are given for the Riesz constants and both a non-adaptive and an adapti...
full textGeneralized B-spline functions method for solving optimal control problems
In this paper we introduce a numerical approach that solves optimal control problems (OCPs) using collocation methods. This approach is based upon B-spline functions. The derivative matrices between any two families of B-spline functions are utilized to reduce the solution of OCPs to the solution of nonlinear optimization problems. Numerical experiments confirm our heoretical findings.
full textgeneralized b-spline functions method for solving optimal control problems
in this paper we introduce a numerical approach that solves optimal control problems (ocps)using collocation methods. this approach is based upon b-spline functions.the derivative matrices between any two families of b-spline functions are utilized toreduce the solution of ocps to the solution of nonlinear optimization problems.numerical experiments confirm our theoretical findings.
full textBiorthogonal Spline Wavelets on the Interval
We investigate biorthogonal spline wavelets on the interval. We give sufficient and necessary conditions for the reconstruction and decomposition matrices to be sparse. Furthermore, we give numerical estimates for the Riesz stability of such bases. §
full textMy Resources
Journal title
volume 4 issue 2
pages 99- 115
publication date 2016-04-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023