Abstract




 
   

IJE TRANSACTIONS B: Applications Vol. 26, No. 11 (November 2013) 1307-1322   

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  USING MODIFIED IPSO-SQP ALGORITHM TO SOLVE NONLINEAR TIME OPTIMAL BANG-BANG CONTROL PROBLEM
 
T. Taleshian, A. Ranjbar and R. Ghaderi
 
( Received: October 05, 2012 – Accepted: April 18, 2013 )
 
 

Abstract    In this paper, an intelligent-gradient based algorithm is proposed to solve time optimal bang-bang control problem. The proposed algorithm is a combination of an intelligent algorithm called improved particle swarm optimization algorithm (IPSO) in the first stage of optimization process together with a gradient-based algorithm called successive quadratic programming method (SQP) in the second stage of the process. The proposed algorithm is called MIPSO-SQP algorithm which in essence is a modification of the previous IPSO-SQP algorithm (PIPSO-SQP). New steps in optimization process of the proposed MIPSO-SQP algorithm causes the algorithm to reach to global optimal solution regardless of any guess of the initial control input and/or the number of switching. Validity of results is verified through adding some arcs to present arcs. The proposed algorithm is successfully applied in time optimal bang-bang control of the Van Der Pol equations, Rayleigh system and F8 aircraft model. A comparison study is also performed to assess the performance of MIPSO-SQP with respect of PIPSO-SQP. It is shown that MIPSO-SQP algorithm is more effective than PIPSO-SQP algorithm due to ability to find global optimum solution in less iteration and in a more systematic way.

 

Keywords    MIPSO-SQP Algorithm, Time Optimal Bang-Bang Control, Nonlinear Systems, Intelligent algorithm, Gradients-Based Algorithm

 

چکیده    در این مقاله الگوریتم هوشمند-گرادیان برای حل مسائل کنترل بنگ-بنگ زمان بهینه ارائه شده است. الگوریتم ارائه شده ترکیبی است از یک الگوریتم هوشمند به نام الگوریتم ارتقا یافته بهینه سازی اجتماع ذرات (IPSO) در مرحله اول جستجو و به دنبال آن در مرحله دوم، الگوریتم گرادیانی به نام روش برنامه ریزی مربعی متوالی (SQP). الگوریتم ارائه شده، MIPSO-SQP نامیده می­شود که در واقع صورت ارتقا یافته الگوریتم قبلی IPSO-SQP (PIPSO-SQP) است. گام­های جدد اضافه شده در پروسه بهینه­سازی الگوریتم MIPSO-SQP ارائه شد سبب شده است که الگوریتم صرف نظر از هر ورودی کنترلی اولیه و تعداد کلیدزنی به پاسخ بهینه کلی دست یابد. صحت نتایج بدست آمده از طریق اضافه کردن تعدادی کمان به کمان­های موجود انجام میگیرد. الگوریتم ارائه شده بطور موفقیت­آمیز در کنترل زمان بهینه معادلات وندرپل، سیستم رایلی و مدل یک هواپیمای F8 بکار گرفته شده است. برای بررسی عملکرد الگوریتم ارائه شده مقایسه­ای نیز با الگوریتم­های کلیدزنی زمان بهینه (TOS) ، روش برنامه­ریزی ریاضی و الگوریتم PIPSO-SQP انجام گرفته است. نشان داده شده است که الگوریتم MIPSO-SQP به دلیل توانایی در پیدا کردن پاسخ بهینه کلی در تعداد تکرارهای کمتر و بصورت سیستماتیک­تر از این الگوریتم­ها موثر­تر است.

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