کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6952528 1451791 2018 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems
ترجمه فارسی عنوان
یک روش مستقیم جدید مبتنی بر توابع کاردانی چبیشف برای مشکلات کنترل بهینه به صورت قطعی متغیر است
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر پردازش سیگنال
چکیده انگلیسی
In this paper, a new direct method based on the Chebyshev cardinal functions is proposed to solve a class of variable-order fractional optimal control problems (V-OFOCPs). To this end, a new operational matrix (OM) of variable-order (V-O) fractional derivative in the Caputo sense is derived for these basis functions and is used to obtain an approximate solution for the problem under study. In the proposed method, the state and the control variables are expanded in terms of the Chebyshev cardinal functions with unknown coefficients, at first. Then, the OM of V-O fractional derivative and some properties of the Chebyshev cardinal functions are employed to achieve a nonlinear algebraic equation corresponding to the performance index and a nonlinear system of algebraic equations corresponding to the dynamical system in terms of the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations derived from the given dynamical system and the initial conditions to the performance index by a set of undetermined Lagrange multipliers. As a result, the necessary conditions of optimality are derived as a system of algebraic equations in the unknown coefficients of the state variable, control variable, and Lagrange multipliers. Furthermore, some numerical examples of different types are demonstrated with their approximate solutions for confirming the high accuracy and applicability of the proposed method.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of the Franklin Institute - Volume 355, Issue 12, August 2018, Pages 4970-4995
نویسندگان
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