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Synchronization of Chaotic Systems with Uncertain Time-Varying Parameters

Ahmad Al-Jarrah(1*), Mohammad Ababneh(2), Suleiman Bani Hani(3), Khalid Al-Widyan(4)

(1) Department of Mechatronics Engineering, Hashemite University, Jordan
(2) Department of Mechatronics Engineering, Hashemite University, Jordan
(3) Department of Mechatronics Engineering, Hashemite University, Jordan
(4) Department of Mechatronics Engineering, Hashemite University, Jordan
(*) Corresponding author



In this paper, a method for digitally redesign of observer-based synchronization for chaotic systems with uncertain time-varying parameters is presented. The proposed design methodology in this work can be considered as an observer design problem where two systems states synchronize. The proposed method starts by having the system in a form suitable for the design; hence, the optimal linearization method (OLM) of the nominal system, around each operating point of the system trajectory, is used. The uncertain time-varying parameters terms are decomposed such that the nonlinear system can be presented as a set of local linear model with disturbed inputs. Then, H∞ robust observer is designed in continuous-time domain based on the linearized model of the system to force the system to synchronize. Finally, a robust digital observer is obtained as a result of applying digital redesign of the designed continuous-time H∞ robust observer using the state matching technique. The effectiveness of the proposed design method is illustrated through numerical examples solving the Chua and Chen chaotic systems. The examples are numerically simulated with Matlab® using a Runge Kutta fourth-order algorithm. The results are provided at the end and then compared with others to show the effectiveness of this method. The results show a robust performance of the proposed method where the trajectory of the states for the drive and response systems synchronizes.
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Synchronized Systems; Control System Design; Digital Redesign; Chaotic Systems; Discrete Systems

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