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Solution of Fractional Optimal Control Problems with Noise Function Using the Bernstein Functions | ||
| Control and Optimization in Applied Mathematics | ||
| دوره 4، شماره 1، مهر 2019، صفحه 37-51 اصل مقاله (385.72 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2020.33909.1078 | ||
| نویسندگان | ||
| Ali Nemati* 1؛ Ali Alizadeh2؛ Fahime Soltanian2 | ||
| 1Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran. | ||
| 2Department of Mathematics, University of Payame Noor, Tehran, Iran | ||
| چکیده | ||
| This paper presents a numerical solution of a class of fractional optimal control problems (FOCPs) in a bounded domain having a noise function by the spectral Ritz method. The Bernstein polynomials with the fractional operational matrix are applied to approximate the unknown functions. By substituting these estimated functions into the cost functional, an unconstrained nonlinear optimization problem is achieved. In order to solve this optimization problem, the Matlab software and its optimization toolbox are used. In the considered FOCP, the performance index is expressed as a function of both state and control functions. The method is robust enough because of its computational consistency in the presence of the noise function. Moreover, the proposed scheme has a good pliability satisfying the given initial and boundary conditions. At last, some test problems are investigated to confirm the efficiency and applicability of the new method. | ||
| کلیدواژه‌ها | ||
| Optimization؛ Spectral method؛ Noise function؛ Fractional optimal control؛ Operational matrix | ||
| عنوان مقاله [English] | ||
| حل مسائل کنترل بهینه کسری دارای تابع نویز با استفاده از توابع برنشتاین | ||
| نویسندگان [English] | ||
| علی نعمتی1؛ علی علیزاده2؛ فهیمه سلطانیان2 | ||
| 1دانشگاه آزاد اسلامی اردبیل | ||
| 2دانشگاه پیام نور، تهران، ایران | ||
| چکیده [English] | ||
| این مقاله، روشی عددی برپایه روش طیفی ریتز را برای حل دسته‌ای از مسائل کنترل بهینه کسری در دامنه محدود دارای نویز بکار می‌برد. پایه‌های چندجمله‌ای برنشتاین به همراه ماتریس عملیاتی مشتق برای تخمین توابع نامعین حالت و کنترل مورد استفاده قرار می گیرند. با جایگذاری توابع تخمینی کنترل و حالت در تابع هدف، یک مساله بهینه‌سازی نامقید ایجاد می‌شود. برای حل و شبیه‌سازی آن از نرم‌افزار \lr{Matlab} و جعبه ابزارهای آن استفاده خواهد شد. در مسائل مورد بحث، تابع هدف شامل توابع کنترل و توابع حالت می‌باشد. روش پیشنهادی با توجه به سازگاری آن در مدیریت شرایط اولیه و مرزی و نویز، قابل اعتماد و اطمینان است. برای نشان دادن کارآیی و کاربردی بودن روش، چند مثال کاربردی در انتهای مقاله آورده شده است. | ||
| کلیدواژه‌ها [English] | ||
| بهینه سازی, روش طیفی, تابع نویز, مساله کنترل بهینه کسری, ماتریس عملیاتی | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 434 تعداد دریافت فایل اصل مقاله: 339 |
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