TITLE

A posteriori error estimates for the fractional optimal control problems

AUTHOR(S)
Ye, Xingyang; Xu, Chuanju
PUB. DATE
September 2015
SOURCE
Journal of Inequalities & Applications;9/9/2015, Vol. 2015 Issue 1, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
In this paper, we study the spectral approximation for a constrained optimal control problem governed by the time fractional diffusion equation. A posteriori error estimates are obtained for both the state and the control approximations. Some numerical experiments are carried out to show that the obtained a posteriori error estimates are reliable.
ACCESSION #
109465933

 

Related Articles

  • Residual Based A Posteriori Error Estimates for Convex Optimal Control Problems Governed by Stokes-Darcy Equations. Ming Cui; Ningning Yan // Numerical Mathematics: Theory, Methods & Applications;Nov2012, Vol. 5 Issue 4, p602 

    In this paper, we derive a posteriori error estimates for finite element ap-proximations of the optimal control problems governed by the Stokes-Darcy system. We obtain a posteriori error estimators for both the state and the control based on the resid-ual of the finite element approximation. It...

  • A POSTERIORI ERROR ESTIMATE OF FINITE ELEMENT METHOD FOR THE OPTIMAL CONTROL WITH THE STATIONARY BÉNARD PROBLEM. Yanzhen Chang; Danping Yang // Journal of Computational Mathematics;Jan2013, Vol. 31 Issue 1, p68 

    In this paper, we consider the adaptive finite element approximation for the distributed optimal control associated with the stationary Bénard problem under the pointwise control constraint. The states and co-states are approximated by polynomial functions of lowest-order mixed finite element...

  • CONSTRUCTION OF INITIAL APPROXIMATION AND METHOD OF COMPUTING OPTIMAL CONTROL. ALEKSANDROV, V. M. // Sibirskie Elektronnye Matematicheskie Izvestiia;2014, Vol. 11, p87 

    A method of reducing computational cost in the course of the control is considered. It is based on subdividing the whole computational process into the computations performed beforehand and those that are carried on while the control takes place. A method of calculation of initial approximation...

  • Numerical Solutions to the Bellman Equation of Optimal Control. Aguilar, Cesar; Krener, Arthur // Journal of Optimization Theory & Applications;Feb2014, Vol. 160 Issue 2, p527 

    In this paper, we present a numerical algorithm to compute high-order approximate solutions to Bellman's dynamic programming equation that arises in the optimal stabilization of discrete-time nonlinear control systems. The method uses a patchy technique to build local Taylor polynomial...

  • A new optimal method of fourth-order convergence for solving nonlinear equations. Lotfi, T. // International Journal of Industrial Mathematics;Spring2014, Vol. 6 Issue 2, p121 

    In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence,...

  • Approximate maximum principle for discrete approximations of optimal control systems with nonsmooth objectives and endpoint constraints. Mordukhovich, Boris S.; Shvartsman, Ilya // ESAIM: Control, Optimisation & Calculus of Variations;Jul2013, Vol. 19 Issue 3, p811 

    The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate...

  • Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian. Simão Antunes, Pedro Ricardo; Freitas, Pedro; Kennedy, James Bernard // ESAIM: Control, Optimisation & Calculus of Variations;Apr2013, Vol. 19 Issue 2, p438 

    We consider the problem of minimising the nth-eigenvalue of the Robin Laplacian in RN. Although for n = 1,2 and a positive boundary parameter α it is known that the minimisers do not depend on α, we demonstrate numerically that this will not always be the case and illustrate how the...

  • EQUIVALENT A POSTERIORI ERROR ESTIMATES FOR A CONSTRAINED OPTIMAL CONTROL PROBLEM GOVERNED BY PARABOLIC EQUATIONS. TONGJUN SUN; LIANG GE; WENBIN LIU // International Journal of Numerical Analysis & Modeling;2013, Vol. 10 Issue 1, p1 

    In this paper, we study adaptive finite element approximation in the backward Euler scheme for a constrained optimal control problem by parabolic equations on multi-meshes. The control constraint is given in an integral sense: K = {u(t) ∈ L2(Ω) : a ≤ JΩ u(t) ≤ b}. We...

  • Approximation of bi-variate functions: singular value decomposition versus sparse grids. Griebel, Michael; Harbrecht, Helmut // IMA Journal of Numerical Analysis;Jan2014, Vol. 34 Issue 1, p28 

    We compare the cost complexities of two approximation schemes for functions f∈Hp(Ω1×Ω2) which live on the product domain Ω1×Ω2 of sufficiently smooth domains Ω1⊂ℝn1 and Ω2⊂ℝn2, namely the singular value/Karhunen–Lòeve decomposition...

Share

Read the Article

Courtesy of MICHIGAN ELIBRARY

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics