Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/29430
Title: Application of Bernoulli polynomials for solving variable-order fractional optimal control-affine problems
Author: Nemati, Somayeh
Torres, Delfim F. M.
Keywords: Variable-order fractional calculus
Bernoulli polynomials
Optimal control-affine problems
Operational matrix of fractional integration
Issue Date: 2020
Publisher: MDPI
Abstract: We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann--Liouville integral operator is used in our new techniques. An accurate operational matrix of variable-order fractional integration for Bernoulli polynomials is introduced. Our methods proceed as follows. First, a specific approximation of the differentiation order of the state function is considered, in terms of Bernoulli polynomials. Such approximation, together with the initial conditions, help us to obtain some approximations for the other existing functions in the dynamical control-affine system. Using these approximations, and the Gauss--Legendre integration formula, the problem is reduced to a system of nonlinear algebraic equations. Some error bounds are then given for the approximate optimal state and control functions, which allow us to obtain an error bound for the approximate value of the performance index. We end by solving some test problems, which demonstrate the high accuracy of our results.
Peer review: yes
URI: http://hdl.handle.net/10773/29430
DOI: 10.3390/axioms9040114
Publisher Version: https://www.mdpi.com/2075-1680/9/4/114
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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