تحلیل پایداری لیاپانوف در آموزش سیستم فازی- عصبی نوع 2 با یک الگوریتم ترکیبی مبتنی بر گرادیان نزولی و فیلتر کالمن

نوع مقاله : مقاله برق

نویسندگان

1 دانشکده مهندسی مکانیک، برق و کامپیوتر، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران

2 گروه مکاترونیک- دانشکده مهندسی برق - دانشگاه صنعتی خواجه نصیرالدین طوسی - تهران- ایران

3 استادیار، دانشکده مهندسی مکانیک، برق و کامپیوتر، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران

چکیده

پایداری آموزش در شناسایی سیستم‌های غیرخطی یکی از مهمترین مسائل در پژوهش های مربوط به کنترل است. این مقاله به بررسی پایداری یک سیستم فازی- عصبی نوع 2 بازه‌ای (IT2ANFIS) به عنوان شناساگر از طریق یک تابع لیاپانوف جدید می‌پردازد. در این تحلیل، آموزش قسمت مقدم و تالی سیستم IT2ANFIS به ترتیب با الگوریتم‌های گرادیان نزولی و فیلتر کالمن صورت می‌پذیرد. از این رو، با استفاده از تابع لیاپانوف مورد نظر، محدوده‌های مجاز متغیر‌های قابل تنظیم آموزش، بدست می‌آیند و بر الگوریتم ها اعمال می‌گردند تا فرآیند شناسایی پایدار بماند. مطابق با تحلیل پایداری این پژوهش، محدوده‌های تطبیقی وسیعی از متغیر‌های قابل تنظیم در آموزش الگوریتم‌ها بدست آمده است. علاوه بر این، مطابق با نتایج شبیه‌سازی، با انتخاب محدوده‌های مجاز بر مبنای تحلیل پایداری پیشنهادی ، فرآیند شناسایی پایدار و با عملکرد مناسبی بوده است. هنگامی که روش پیشنهادی برای پیش‌بینی مقادیر آتی سری آشوب مکی‌گلاس و یک سیستم غیرخطی با داده‌های تصادفی به کار گرفته می‌شود، از نظر ریشه دوم میانگین خطا، زمان شناسایی، و قرار‌گیری در تله کمینه محلی عملکرد بهتری نسبت به روش‌های دیگر دارد.

کلیدواژه‌ها


عنوان مقاله [English]

Lyapunov stability analysis in the training of type 2 neuro-fuzzy inference system with a hybrid algorithm based on gradient descent and Kalman filter

نویسندگان [English]

  • Mohammad Mahdi Zabihi Shesh Poli 1
  • Mahdi Aliyari Shoorehdeli 2
  • Ali Moarefianpour 3
1 Department of Mechanical, Electrical and Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Department of electrical engineering,- K. N. Toosi University of Technology,-Tehran-Iran
3 Department of Mechanical, Electrical and Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
چکیده [English]

The stability of the training process in the identification of nonlinear systems is one of the foremost issues in control research. This paper studies the training stability of an interval type 2 adaptive neuro-fuzzy Inference system (IT2ANFIS) as an identifier through a newfound Lyapunov function. Lyapunov stability analysis is conducted on the training of IT2ANFIS, when the premise and the consequent of the system are trained with the gradient descent algorithm and the Kalman Filter, respectively. Therefore, using the proposed stability analysis, the permissible limits for the adjustable parameters of the algorithms are applied to the algorithms to maintain the stability of the identification process. According to the stability analysis of this study, wide ranges of adaptive limits are obtained for the adjustable parameters of the algorithms. Besides, the simulation results show that when the permissible limits are chosen based on the proposed stability analysis, the identification process is stable with acceptable performance. The proposed method outperforms other methods in terms of root mean square error, simulation time, and its less stagnation in the trap of local minimums when it is utilized in the training of the Mackey-Glass chaotic time series and a nonlinear plant with stochastic data sets.

کلیدواژه‌ها [English]

  • System identification
  • Lyapunov stability
  • IT2ANFIS
  • gradient descent
  • Kalman filter
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