The switching fractional order chaotic system and its application to image encryption

Hou, Jialin; Rui, Xiaoting; Liu, Ping; Liu, Tianliang

doi:10.1109/jas.2016.7510127

Cited by 41 publications

(18 citation statements)

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“…Therefore, according to Lemma 5, all the states of system (10) are globally and asymptotically stable, and tracking errors ( = 1, ⋅ ⋅ ⋅ , ) will converge to zero asymptotically under the proposed control scheme. The proof is completed.…”

Section: Controller Designmentioning

confidence: 91%

“…where system orders ∈ (0, 1) are not all the same. = [ 1 , ⋅ ⋅ ⋅ , ] T is the state vector, is controller input, and is the output of system (10). ∈ R ( = 1, ⋅ ⋅ ⋅ , − 1) is the vector of unknown constant parameters.…”

Section: Controller Designmentioning

confidence: 99%

“…Obviously, noncommensurate fractional-order ferroresonance system (8) is a particular case of the strict-feedback noncommensurate fractional-order system with unknown parameters (10). To design an excellent adaptive backstepping controller for system (10), in each step, a virtual controller and parameter update law are designed systematically until the last equation which contains the controller.…”

Section: Controller Designmentioning

confidence: 99%

“…Fractional calculus can provide clearer and more accurate description than the classical calculus methods without memory which is only a particular case. Furthermore, with the help of fractional-order calculus, we can obtain more accurate descriptions of the physical phenomena, such as electrical circuit [3,4], power system [5,6], signal processing [7], secure communication [8], bioengineering [9], and image encryption [10]. Second, the fractional-order can enhance the flexibility of parameters and reveal various unusual characteristics of the fractionalorder system and fractional-order controllers which remain concealed in the integer-order method.…”

Section: Introductionmentioning

confidence: 99%

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Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System

Wang

Liu

et al. 2018

Mathematical Problems in Engineering

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In this paper, fractional calculus is applied to establish a novel fractional-order ferroresonance model with fractional-order magnetizing inductance and capacitance. Some basic dynamic behaviors of this fractional-order ferroresonance system are investigated. And then, considering noncommensurate orders of inductance and capacitance and unknown parameters in an actual ferroresonance system, this paper presents a novel fractional-order adaptive backstepping control strategy for a class of noncommensurate fractional-order systems with multiple unknown parameters. The virtual control laws and parameter update laws are designed in each step. Thereafter, a novel fractional-order adaptive controller is designed in terms of the fractional Lyapunov stability theorem. The proposed control strategy requires only one control input and can force the output of the chaotic system to track the reference signal asymptotically. Finally, the proposed method is applied to a noncommensurate fractional-order ferroresonance system with multiple unknown parameters. Numerical simulation confirms the effectiveness of the proposed method. In addition, the proposed control strategy also applies to commensurate fractional-order systems with unknown parameters.

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Section: Controller Designmentioning

confidence: 91%

Section: Controller Designmentioning

confidence: 99%

Section: Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System

Wang

Liu

et al. 2018

Mathematical Problems in Engineering

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“…Compared with integer order chaotic systems, fractional-order chaotic systems have more complex chaotic characteristics and more complicated topological structures. When applied to image encryption, the fractional-order systems could support a larger key space, enhance security and withstand the attacks effectively [22,23].…”

Section: Introductionmentioning

confidence: 99%

Multi‐switching combination–combination synchronization of non‐identical fractional‐order chaotic systems

Khan

Bhat

2017

Math Methods in App Sciences

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In this paper, multi-switching combination-combination synchronization scheme has been investigated between a class of four non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen's systems are taken as drive systems. The combination-combination of multi drive systems is then synchronized with the combination of fractionalorder Lü and Rössler chaotic systems. In multi-switching combination-combination synchronization, the state variables of two drive systems synchronize with different state variables of two response systems simultaneously. Based on the stability of fractional-order chaotic systems, the multi-switching combination-combination synchronization of four fractional-order non-identical systems has been investigated. For the synchronization of four non-identical fractionalorder chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

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Chaotic Image Encryption: State-of-the-Art, Ecosystem, and the Promise of Quantum-Inspired AI

Zolfaghari,

Nemati,

Yanai

et al. 2023

Crypto and AI

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The switching fractional order chaotic system and its application to image encryption

Cited by 41 publications

References 0 publications

Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System

Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System

Multi‐switching combination–combination synchronization of non‐identical fractional‐order chaotic systems

Chaotic Image Encryption: State-of-the-Art, Ecosystem, and the Promise of Quantum-Inspired AI

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