Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 26, No. 11 (November 2013) 1299-1306   

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  SUPPRESSION OF CHAOTIC BEHAVIOR IN DUFFING-HOLMES SYSTEM USING BACKSTEPPING CONTROLLER OPTIMIZED BY UNIFIED PARTICLE SWARM OPTIMIZATION ALGORITHM
 
R. Gholipour, A. Khosravi and H. Mojallali
 
( Received: October 07, 2012 – Accepted in Revised Form: February 28, 2013 )
 
 

Abstract    The nonlinear behavior analysis and chaos control for Duffing-Holmes chaotic system is discussed in the paper. In order to suppress the irregular chaotic motion, an optimal backstepping controller is designed. The backstepping method consists of parameters with positive values. The improper selection of the parameters leads to inappropriate responses or even may lead to instability of the system. In this paper, the Unified particle swarm optimization (UPSO) algorithm is utilized to determine the convenient and optimal values of the parameters. The minimized objective function via UPSO algorithm is a weighted sum of the Integral of Time multiplied Absolute Error (ITAE) and squared control signal. Fast control of chaos in a very short time and having more limited control signal for this purpose, are the great advantages of the proposed controller. Numerical simulations show the high performance of this method for chaos elimination in Duffing-Holmes system.

 

Keywords    Duffing-Holmes system, control of chaos, backstepping controller, UPSO algorithm

 

چکیده    چكيده آنالیز رفتار غیر خطی و کنترلِ آشوب برای سیستم آشوبی دافینگ-هولمس، در مقاله بحث شده است. برای فرو نشاندن (حذف) حرکت آشوبی نا منظم، یک کنترل کننده پسگام بهینه طراحی می شود. روش پسگام شامل پارامترهایی با مقادیر مثبت است. انتخاب نا مناسب پارامترها منجر به پاسخ های نا مناسب یا حتی ممکن است منجر به ناپایداری سیستم شود. در این مقاله، الگوریتم بهینه سازی اجتماع ذرات یکپارچه، برای تعیین مقادیر مناسب و بهینه ی پارامترها استفاده می شود. تابع هدف مینیمم شده توسط الگوریتم بهینه سازی اجتماع ذرات یکپارچه، یک مجموع وزنی از انتگرال زمان ضربدر قدر مطلق خطا و مربع سیگنال کنترلی است. کنترل سریع آشوب در یک زمان خیلی کوتاه و داشتن سیگنال کنترلی محدود برای این کار از مزیت های بزرگ کنترل کننده پیشنهادی هستند. شبیه سازیهای عددی کارامدی بالای این روش را برای حذفِ آشوب در سیستم دافینگ- هولمس نشان می دهند.

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