An Adaptive Synchronization Method for Fractional Heterogeneous Structure Chaotic System

Abstract

The invention discloses an adaptive synchronization method for a fractional-order chaotic system with different structures. The main steps are: (1) selecting two fractional-order chaotic systems with different structures and definite parameters as the drive system and the response system; (2) calculating Score fractional error system e 1 , e 2 , e 3 , e 4 ; (3) In the fractional order error system e 1 , e 2 , e 3 , e 4 , add u respectively 1 (t), u 2 (t), u 3 (t), u 4 (t) controller; (4) design u 1 (t), u 2 (t), u 3 (t), u 4 (t) Controller and adaptive law; (5) Construct Lyapunov control function, use the properties of Caputo derivative operator combined with Mittag‑Leffler stability theory to judge the fractional error system e 1 , e 2 , e 3 , e 4 It is asymptotically stable and realizes synchronous control of chaotic systems with different structures under certain parameters. The present invention can effectively control the fractional-order chaotic system with deterministic parameters. By designing an adaptive controller, the constructed Lyapunov function is combined with the fractional-order Mittag-Leffler stability theory, which effectively reduces the complexity of control and shortens the synchronization time. Time is a universal control method.

Description

An Adaptive Synchronization Method for Fractional Heterogeneous Structure Chaotic System technical field What the present invention relates to is a kind of synchronization method of fractional order heterostructure chaotic system, belongs to automatic control method technology field. Background technique Due to the very rich dynamic characteristics of nonlinear chaotic systems, it has been applied in many fields. applications in fields such as meteorology, mechanics, and secure communications. It has a very wide range of applications in mixed security communication and related scientific fields. The prospect of chaotic synchronization is the key technology. Since the 1990s, the US Naval Laboratory Pecora and Carroll proposed Since the concept of chaotic synchronization, many scholars have proposed many effective synchronization methods, such as drive-response synchronization, active-by-pass synchronization Dynamic synchronization, coupling synchronization, adapti...

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Problems solved by technology

The document "Adaptive feedback control and synchronization of non-identical chaotic fractional order systems" realizes adaptive synchronous control of fractional order systems by looking for inequality substitution methods, and the document "Finite-time synchronization between two complex-variable chaotic systems with unknown parameters via nonsingular terminal Sliding modecontrol" and the document "Synchronization of Chaotic Fractional-Order Systems via Fractional-Order Adaptive Controller" are converted by constructing a sliding mode control surface. The mathematical operation process of these two methods is cumbersome, and currently lacks a more universal application for fractional order chaotic systems. Adaptive Synchronous Control Method

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