Solution for fractional distributed optimal control problem by hybrid meshless method

Abstract

We use a hybrid local meshless method to solve the distributed optimal control problem of a system governed by parabolic partial differential equations with Caputo fractional time derivatives of order α ∈ (0, 1]. The presented meshless method is based on the linear combination of moving least squares and radial basis functions in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of coupled fractional partial differential equations, with necessary and sufficient conditions, for fractional distributed optimal control problems using a combination of moving least squares and radial basis functions. To keep matters simple, the problem has been considered in the one-dimensional case, however the techniques can be employed for both the two- and three-dimensional cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed method.

Fractional-order Lagrange polynomials: An application for solving delay fractional optimal control problems

“…The importance of optimal control problems has led to the development of various analytical and numerical methods to solve these problems. Several efficient numerical methods for solving fractional optimal control problems such as Bernoulli polynomials (Keshavarz et al, 2015), Boubaker polynomials (Rabiei et al, 2017b), multiwavelets (Lotfi, 2011; Yousefi et al, 2011), the Ritz-variational method (Lotfi and Yousefi, 2017), the modified Adomian decomposition method (Alizadeh and Effati, 2017), the hybrid meshless method (Darehmiraki et al, 2018), the finite element method (Zhou and Gong, 2016), methods based on eigenfunctions Özdemir et al, 2009), etc. have been developed.…”

An artificial neural network‐based method for the optimal control problem governed by the fractional parabolic equation

“…Because lim n→∞ w(t n ) =ŵ, there exist a t i , such thatq(w(t i )) ≤ . Using Lemma 5.1, we obtain 1 2 ||w(t) −ŵ|| 2 ≤q(w(t)) andŵ is non-increasing. Thus, t ≥ t i , we obtain 1 2…”

“…Some applications of fractional derivatives can be found in References [8][9][10][11][12][13]. The main purpose of this paper is to solve a class of optimal control problem governed by a fractional parabolic equation as following [1] min J = 1 2 ∫…”

A solution for fractional PDE constrained optimization problems using reduced basis method

“…A new spectral collocation algorithm for solving time-space fractional partial differential equations with subdiffusion was reported in Bhrawy (2016). A hybrid meshless method was proposed for FODCP in Darehmiraki et al (2016). Zacky and Mchado Zaky and Machado (2017) provided a solution for FODCP by pseudo-spectral method.…”