18 خرداد 1402
سميه نعمتي

سمیه نعمتی

مرتبه علمی: دانشیار
نشانی:
تحصیلات: دکترای تخصصی / ریاضی کاربردی
تلفن: 01135302419
دانشکده: دانشکده علوم ریاضی

مشخصات پژوهش

عنوان Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
variable-order fractional calculus; Bernoulli polynomials; optimal control-affine problems; operational matrix of fractional integration
مجله Axioms
شناسه DOI 10.3390/axioms9040114
پژوهشگران سمیه نعمتی (نفر اول) ، دلفیم تورس (نفر دوم)

چکیده

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.