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Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 1، دوره 2، شماره 2، اسفند 2017، صفحه 1-14 اصل مقاله (694.44 K) | ||
| نوع مقاله: Research Article | ||
| نویسنده | ||
| Saeed Nezhadhosein* | ||
| Department of Applied Mathematics, Payame Noor University, Tehran, 193953697, Iran | ||
| چکیده | ||
| In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations, as Haar matrix equations using Kronecker product. Then the error analysis of the proposed method is presented. Some numerical examples are given to demonstrate the efficiency of the method. The solutions converge as the number of approximate terms increase. | ||
| کلیدواژه‌ها | ||
| Time-variant linear-quadratic optimal control problems؛ Matrix algebraic equation؛ Haar wavelet | ||
| عنوان مقاله [English] | ||
| معادلات ماتریسی هار برای حل مسائل کنترل بهینه درجه دوم خطی وابسته به زمان | ||
| چکیده [English] | ||
| در این مقاله موجک‌های هار برای حل مسائل کنترل بهینه وابسته به زمان درجه دوم خطی زمان پیوسته به کار رفته است. ابتدا با شرایط لازم بهینگی مساله به یک مساله مقدار مرزی دونقطه‌ای TBVP تبدیل می‌شود. سپس موجک‌های هار برای تبدیل TBVP، به‌عنوان یک سیستم از معادلات دیفرانسیلی، به یک سیستم معادلات جبری ماتریسی، به‌عنوان معادلات ماتریسی هار با ضرب کرونکر، تبدیل می‌شود. تحلیل خطای روش پیشنهادی ارائه شده است. جواب‌ها با افزایش تعداد جملات تقریب همگرا می‌شود | ||
| کلیدواژه‌ها [English] | ||
| مسائل کنترل بهینه درجه دوم خطی وابسته به زمان, معادله جبری ماتریسی, موجک هار | ||
| مراجع | ||
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