Adaptive modified function projective synchronization for a chaotic complex system

Subject Areas : Statistics

Moosarreza  Shamsyeh Zahedi ¹ (Department of Mathematics, Payame Noor University (PNU), P.O. BOX 19395-4697, Tehran, Iran)

Received: 2021-03-07 Accepted : 2021-07-06 Published : 2022-01-21

Keywords: پایداری لیاپانف, دستگاه آشوبناک با متغیرهای مختلط&rlm, , &lrm, &lrm, &rlm, همزمان&lrm, سازی تابع تصویری&rlm, ,

Abstract :

‎This ‎paper ‎presents ‎the‎ modified function projective synchronization (MFPS) in a system with complex variables related to the permanent magnet synchronous motor (PMSM) with unknown parameters.‎ In this method, by defining a suitable adaptive controller and other desired functions and with the aid of Lyapunov stability theory, the asymptotic stability of the error function can be proved. This can lead to a modified function projective synchronization between two complex chaotic systems with completely unknown parameters. Also, the error of estimating the parameters and the value of the coupling strength is accurately expressed using the proposed method.‎‎Because in the modified projective synchronization (MPS) and function projective synchronization (FPS) methods, fixed coupling strength is considered, this limits the range of applications of these methods. MFPS is, therefore, a more general definition of MPS and FPS when the scaling function matrix is chosen by a constant matrix and a scaling function, respectively. This method can be used on other complex dynamic systems. Numerical simulations are presented to show the effectiveness and validity of the above theoretical results.

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