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Enlarging the Region of Attraction for Nonlinear Systems through the Sum-of-Squares Programming | ||
| Control and Optimization in Applied Mathematics | ||
| دوره 4، شماره 2، فروردین 2019، صفحه 19-37 اصل مقاله (558.38 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.30473/coam.2020.53510.1141 | ||
| نویسندگان | ||
| Jahangir Alizadeh1؛ Hamid Khaloozadeh* 2 | ||
| 1Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-3697, Tehran, Iran | ||
| 2Professor of Systems and Control Engineering, KN Toosi University of Technology, Tehran, Iran | ||
| چکیده | ||
| In the present study, a novel methodology is developed to enlarge the Region of Attraction (ROA) at the point of equilibrium of an input-affine nonlinear control system. Enlarging the ROA for non-polynomial dynamical systems is developed by designing a nonlinear state feedback controller through the State-Dependent Riccati Equation (SDRE). Consequently, its process is defined in the form of Sum-of-Squares (SOS) optimization problem with control and non-control constraints. Of note, the proposed technique is effective in estimating the ROA for a nonlinear system functioning on polynomial or non-polynomial dynamics. In the present study, the application of the proposed scheme are shown by numerical simulations. | ||
| کلیدواژهها | ||
| State-dependent Riccati equation؛ Region of attraction؛ Sum-of-squares programming؛ Lyapunov function | ||
| عنوان مقاله [English] | ||
| توسیع ناحیه جذب سیستمهای غیرخطی با استفاده از برنامه نویسی مجموع مربعات | ||
| نویسندگان [English] | ||
| جهانگیر علیزاده1؛ حمید خالوزاده2 | ||
| 1مرکز تحصیلات تکمیلی دانشگاه پیام نور تهران | ||
| 2دانشگاه خواجه نصیر طوسی-تهران | ||
| چکیده [English] | ||
| در این پژوهش روشی جدید برای توسیع ناحیه جذب نقطه تعادل یک سیستم کنترل غیرخطی آفین ارائه شده است. برای توسیع ناحیه جذب سیستمهای دینامیکی غیر چندجملهای به کمک طراحی کنترلکننده فیدبک حالت غیرخطی از معادله ریکاتی وابسته به حالت استفاده شده است. فرایند بدست آوردن ناحیه جذب باعث ایجاد یک مسئله بهینه سازی مجموع مربعات با محدودیتهای کنترلی و غیر کنترلی میشود. نکته قابل توجه این است که روش پیشنهادی برای تخمین ناحیه جذب سیستمهای غیرخطی چندجملهای و غیر چندجملهای کارا است. همچنین در این مطالعه کاربرد روش پیشنهادی با شبیه سازیهای عددی نشان داده شده است. | ||
| کلیدواژهها [English] | ||
| معادله ریکاتی وابسته به حالت, ناحیه جذب, فاکتور شکل, برنامهنویسی مجموع مربعات, تابع لیاپانوف | ||
| مراجع | ||
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