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Anew method for finding closed-loop optimal controllers of fractional tracking quadratic optimal control problems is introduced. The optimality conditions for the fractional optimal control problem are obtained. Illustrative examples are…

Optimization and Control · Mathematics 2026-02-03 Iman Malmir

A piecewise constant Mayer cost function is used to model optimal control problems in which the state space is partitioned into several regions, each having its own Mayer cost value. In such a context, the standard numerical methods used in…

Optimization and Control · Mathematics 2021-12-02 P. -Y. Bouchet , C. Audet , L. Bourdin

In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…

Numerical Analysis · Mathematics 2018-01-23 Seshu Kumar Damarla , Madhusree Kundu

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with…

Optimization and Control · Mathematics 2010-10-25 Gastao S. F. Frederico , Delfim F. M. Torres

This paper proposes a new numerical method based on the Chebyshev wavelets (CWs) to solve the variable-order time fractional mobile-immobile advection-dispersion equation. To do this, a new operational matrix of variable-order fractional…

Numerical Analysis · Mathematics 2016-05-23 Mohammad Hossein Heydari

In this paper the singular Emden-Fowler equation of fractional order is introduced and a computational method is proposed for its numerical solution. For the approximation of the solutions we have used Boubaker polynomials and defined the…

Numerical Analysis · Mathematics 2022-02-28 Abdelkrim Bencheikh , Lakhdar Chiter

We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of…

Optimization and Control · Mathematics 2024-04-25 Mikhail Gomoyunov

We consider fractional order optimal control problems in which the dynamic control system involves integer and fractional order derivatives and the terminal time is free. Necessary conditions for a state/control/terminal-time triplet to be…

Optimization and Control · Mathematics 2013-11-01 Shakoor Pooseh , Ricardo Almeida , Delfim F. M. Torres

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…

Numerical Analysis · Mathematics 2020-07-07 Britta Schmitt , Boris N. Khoromskij , Venera Khoromskaia , Volker Schulz

We propose and study an optimal control model for malaria infection described by system of fractional differential equations. The model is formulated in terms of the left and right Caputo fractional derivatives. We determine the necessary…

Dynamical Systems · Mathematics 2016-07-07 E. Okyere , F. T. Oduro , S. K. Amponsah , I. K. Dontwi

We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…

Optimization and Control · Mathematics 2015-04-21 Harbir Antil , Enrique Otarola

A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…

Numerical Analysis · Mathematics 2018-02-01 Seshu Kumar Damarla , Madhusree Kundu

In this paper, we study the numerical approximation of a system of PDEs with fractional time derivatives. This system is derived from an optimal control problem for a time-fractional Fokker-Planck equation with time dependent drift by…

Numerical Analysis · Mathematics 2020-06-08 Fabio Camilli , Serikbolsyn Duisembay , Qing Tang

In this paper, an easy-to-implement and computationally effective numerical method based on the new orthogonal hybrid functions is developed to solve system of fractional order differential equations numerically. The new orthogonal hybrid…

Numerical Analysis · Mathematics 2018-01-23 Seshu Kumar Damarla , Madhusree Kundu

We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…

Optimization and Control · Mathematics 2022-12-07 Jean-Baptiste Caillau , Roberto Ferretti , Emmanuel Trélat , Hasnaa Zidani

We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…

Classical Analysis and ODEs · Mathematics 2012-10-29 Tatiana Odzijewicz , Agnieszka B. Malinowska , Delfim F. M. Torres

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…

General Mathematics · Mathematics 2016-11-03 Ricardo Almeida , Nuno R. O. Bastos , M. Teresa T. Monteiro

Based on a method introduced by Leitmann [Internat. J. Non-Linear Mech. {\bf 2} (1967), 55--59], we exhibit exact solutions for some fractional optimization problems of the calculus of variations and optimal control.

Optimization and Control · Mathematics 2010-09-29 Ricardo Almeida , Delfim F. M. Torres

We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…

Numerical Analysis · Mathematics 2021-06-18 Susanne C. Brenner , Li-yeng Sung , Winnifried Wollner

A Caputo fractional-order mathematical model for the transmission dynamics of tuberculosis (TB) was recently proposed in [Math. Model. Nat. Phenom. 13 (2018), no. 1, Art. 9]. Here, a sensitivity analysis of that model is done, showing the…

Optimization and Control · Mathematics 2019-08-12 Silverio Rosa , Delfim F. M. Torres