Robust adaptive control for fractional-order chaotic systems with system uncertainties and external disturbances

Abstract

This paper studies the robust adaptive control of fractional-order chaotic systems with system uncertainties and bounded external disturbances. Based on a proposed lemma, quadratic Lyapunov functions are used in the stability analysis and fractional-order adaptation laws are designed to update the controller parameters. By employing the fractional-order expansion of classical Lyapunov stability method, a robust controller is designed for fractional-order chaotic systems. The system states asymptotically converge to the origin and all signals in the closed-loop system remain bounded. A counterexample is constructed to show that the fractional-order derivative of a function is less than zero does not mean that the function monotonically decreases (this property appears in many references). Finally, simulation results are presented to confirm our theoretical results.

Adaptive H∞ Observer‐Based Sliding Mode Control for Uncertain Fractional‐Order Nonlinear Systems

“…Fractional-order nonlinear systems which involved non-integer order derivatives can describe the complex dynamic systems with memory and genetic characteristics more accurately such as viscoelastic systems, electrode systems, diffusion process and so on [1][2][3][4]. On the other hand, the actual systems are commonly subject to uncertainties and external disturbances, which may lead to instability of the systems [5,6]. Therefore, the robust control issue for uncertain fractional-order nonlinear systems becomes more inevitable.…”

Design of Clothing with Encrypted Information of Lost Children Information Based on Chaotic System and DNA Theory

“…In addition, such a locator has a large amount of radiation. Moreover, the compliance of the locator also makes it inconvenient to clean clothes and shoes [1][2][3][4][5][6][7][8][9][10]. Therefore, compared with electronic tags and identifi cation cards that rely on radio frequency identifi cation (RFID) technology, we prefer a nonradiation, confi dential identifi cation technology that does not need to rely on network storage.…”

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On the basis of the integer-order chaotic system, we decompose its fractional order, because the fractional-order system has more complex dynamic characteristics, and the security performance of the encryption system designed on this basis is also higher [6][7][8][9]. For instance, Dong et al designed a color image encryption algorithm based on a fractional hyperchaotic system and introduced the compression theory of

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A hybrid adaptive synchronization protocol for nondeterministic perturbed fractional-order chaotic nonlinear systems

“…This is ascribed to that fractional calculus provides not only a powerful algorithmic tool to facilitate complex numerical computing, but also a comprehensive mathematical model of enormous practical problems [2]. In view of heredity and memristive feature, fractional-order calculus can be utilized to model most of complex dynamic behaviors or specific materials (such as chaos, anomalous diffusions, viscoelastic damping structures, neural networks, and so on, see [3][4][5][6][7][8]) more precisely, beyond the integer-order calculus in general. Due to this, the topic of synchronization protocol design for fractional-order nonlinear systems has dramatically stirred plenty of excitement in many research fields.…”