Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

Abstract

Abstract:In this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.PACS (2008)

A fractional approach to the Sturm-Liouville problem

“…In the last three decades, the interest in these operators and their applications has became of great importance in many fields of science and engineering, for example mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing, due to the Fractional Calculus constitutes a meeting place of multiple disciplines: stochastic processes, probability, integro-differential equations, integral transforms, special functions, numerical analysis... These fractional operators are non-local and they have certain capacity of memory associated their convolution kernel, so Fractional Calculus became a powerful framework to model many real processes of anomalous systems ( [4][5][6][7][8]) by using fractional ordinary or partial differential equations and systems of these fractional equations ( [9][10][11][12]). In this sense, the introduction of fractional operators for building a fractional Sturm-Liouville theory can be interesting to generalize the classical theory and to give theoretical support to the numerical results obtained by several authors recently (for example, [13][14][15][16][17][18][19][20][21]).…”

A novel finite‐time terminal observer of a fractional‐order chaotic system with chaos entanglement function

“…2) Delavari and co-authors, 49 investigated the sliding observer for FO systems in Brunovsky canonical form. For simulations, Arnodo-Coullet system with initial condition is taken as x(0) = [−1.2; 1.…”

Adaptive Integral‐Based Robust Q‐S Synchronization and Parameter Identification of Nonlinear Hyperchaotic Complex Systems

“…e sliding mode control (SMC) has attracted researchers' attention in recent years due to its robust response to model insensitivity towards nonlinearities, ease of implementation, low computational cost, and simplicity in feedback design [29][30][31][32][33][34]. Moreover, SMC is independent of external interferences and only depends on the switching surface design (also called the sliding surface) [31].…”