سنکرونسازی آشوب براساس معادلات دیفرانسیل و قضیه تقریب عمومی و کاربرد آن در مخابرات امن و رمزنگاری

نویسندگان

بیرجند

چکیده

در این مقاله، یک روش جدید به‌منظور سنکرون‌سازی آشوب با استفاده از کنترل غیرخطی ارائه شده است. در اکثر کنترل-کننده‌های موجود فرض می‌شود مدل ریاضی سیستم‌های آشوبی فرستنده و گیرنده کاملاً یکسان هستند. با توجه به یکسان‌نبودن شرایط محیطی فرستنده و گیرنده و تاثیر درجه حرارت و سایر عوامل بر پارامترهای سیستم آشوبی از قبیل مقادیر مقاومت‌ها و سایر المان‌ها، یکسان درنظرگرفتن مدل‌های فرستنده و گیرنده معقول نیست. در این مقاله، روش جدیدی برای تخمین عدم قطعیت‌ها ارائه شده است که در آن عدم قطعیت‌ها با یک معادله دیفرانسیل خطی با ضرایب نامعلوم ثابت مدل‌سازی می‌شود. به عبارت دیگر، عدم قطعیت‌ها را می‌توان به‌صورت پاسخ این معادله دیفرانسیل نمایش داد. با توجه به این‌که این تابع (پاسخ معادله دیفرانسیل) شرایط قضیه تقریب عمومی را دارد، می‌توان هر تابع غیرخطی را با دقت دلخواه تخمین زد، اما با توجه به این‌که ضرایب معادله دیفرانسیل نامعلوم می‌باشند، پارامترهای این تابع نیز نامعلوم بوده و باید تخمین زده شوند. این‌کار با استفاده از قوانین تطبیق به‌دست‌آمده از تحلیل همگرایی خطای سنکرون‌سازی انجام می‌‌گردد. نتایج شبیه‌سازی بیانگر عملکرد مناسب تخمین‌گر ارائه شده بوده و در مقایسه با کنترل‌کننده فازی مد لغزشی سرعت پاسخ کنترل‌کننده پیشنهادی بهتر می‌باشد. همچنین، کاربرد آن در مخابرات امن و رمزنگاری مورد بررسی قرار گرفته است.

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