Zaman Gecikmeli Diferansiyel Denklem Tabanlı Kaotik Sistemlerde Çevrimiçi Zaman Gecikmesi Kestirimi

Year 2017, Volume: 3 Issue: 3, 65 - 73, 27.12.2017

Alper Bayrak Enver Tatlıcıoğlu

Abstract

Bu çalışmada, gecikmeli fark denklemleri tabanlı kaotik sistemlerde zaman gecikmesi kestirimi ele alınmıştır. Zaman gecikmesi, sistemin doğrusallığını bozan bir parametre olarak düşünülmüştür. Bu düşünce doğrultusunda, doğrusal olmayan bir kestirim yönteminden faydalanılmıştır. Bu yöntem, Lyapunov kararlılık analizlerine dayanmaktadır ve tüm sinyallerin küresel olarak sınırlı kalmasını ve kestirim hatasının sıfıra yakın bir noktaya yakınsamasını garanti etmektedir. Zaman gecikmesi kestirimi yönteminin etkinliğini göstermek için, birbirinden farklı, gecikmeli fark denklemleri tabanlı kaotik sistem modelleri kullanılarak birden fazla sayısal benzetim çalışmaları yapılmıştır. Sayısal benzetim çalışmaları sonucunda, yöntemin etkili bir şekilde çalıştığı görülmüştür.

Keywords

Kaotik sistemler, Zaman gecikmesi, Kestirim

Online Time Delay Estimation in Delay Differential Equation Based Chaotic Systems

Abstract

In this work, time delay estimation in delay differential equation based chaotic systems is handled. The time delay is handled as a parameter which effects the system nonlinearly. Under the light of this consideration, a nonlinear parameter estimator is utilized. The aforementioned method is based on Lyapunov stability analysis and assures global boundedness of all the signals and the convergence of the estimation error to the vicinity of zero. Several simulations are given to demonstrate the efficiency of the proposed time delay estimator for various delay differential equation based chaotic systems. From the numerical simulation studies, it is observed that the method works efficiently.

Keywords

Chaotic systems, Time delay, Estimation

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