Design of adaptive sliding mode tracking controllers for chaotic synchronization and application to secure communications

Synchronization of two identical chaotic systems with matched and mismatched perturbations by utilizing adaptive sliding mode control (ASMC) technique is presented in this paper. The sliding surface function is specially designed based on the Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. The designed tracking controller can not only suppress the mismatched perturbations when the controlled dynamics (master–slave) are in the sliding mode, but also drive the trajectories of synchronization errors into a small bounded region whose size can be adjusted through the designed parameters. Adaptive mechanisms are employed in the proposed control scheme for adapting the unknown upper bounds of the perturbations, and the stability of overall controlled synchronization systems is guaranteed. The comparison of the proposed chaotic synchronization technique with an existing generalized chaotic synchronization (GCS) method as well as application of the proposed control method to secure communications is also demonstrated in this paper.     

Synchronization of chaotic systems with unknown parameters using adaptive passivity-based control

This paper investigates the problem of complete synchronization of chaotic systems with unknown parameters. An adaptive control scheme based on a feedback passivity approach is proposed. The convergence of the synchronization error is guaranteed. The unified chaotic and hyperchaotic Lü systems are taken as illustrative examples. The feasibility and effectiveness of the proposed scheme are demonstrated through numerical simulations.     

Adaptive single input sliding mode control for hybrid-synchronization of uncertain hyperchaotic Lu systems

This paper addresses the problem of hybrid synchronization for hyperchaotic Lu systems without and with uncertain parameters via a single input sliding mode controller (SMC). Based on the SMC approach, the proposed controller not only minimizes the influence of uncertainty but also enhances the robustness of the system. The uncertain parameters are estimated by using new adaptation laws which ensure the uncertain parameters convergence to their original value. A hybrid synchronization scheme is useful to maintain the vastly secured and secrecy in the area of secure communication by using the control theory approach. The proposed hybrid synchronization results are providing a superiority of forming a chaotic secure communication scheme. Finally, a numerical example is provided to demonstrate the validity of the theoretical analysis.     

A new approach for constrained chaos synchronization with application to secure data communication

In this paper, a new technique is introduced for chaos secure data communication. In this approach, in addition to the usually used techniques for data encryption, the concept of carrier encryption is introduced to increase the security level of the secure communication scheme. To fulfill this objective, at the transmitting end, two chaotic oscillators are coupled, and a set of inequality time dependent constraints with time dependent bounds is imposed on the generated chaotic signals. Moreover, to increase system complexity and its security level, the imposed set of constraints and their bounds are allowed to be changeable from one time period to another during the transmission process. As a result, the patterns of the generated chaotic signals are completely changed and the chaotic oscillator is completely encrypted. At the receiving end, the newly developed Constrained Smoothed Regularized Least Square (CSRLS) observer is used to synchronize the received constrained chaotic signals and hence retrieve the transmitted data. Using such an approach, the quality of the received information, measured by the Bit Error Rate (BER), is highly improved due to the superior performance of the developed CSRLS observer. The stability of the observer is analyzed, and simulation results are presented to show the efficiency and effectiveness of the proposed secure communication scheme.     

Chaotic synchronization between different fractional-order chaotic systems

Based on the idea of tracking control and stability theory of fractional-order systems, a novel synchronization approach for fractional order chaotic systems is proposed. We prove that the synchronization between drive system and response system with different fractional order q can be achieved, and the synchronization between different fractional-order chaotic systems with different fractional order q can be achieved. Two examples are used to illustrate the effectiveness of the proposed synchronization method. Numerical simulations coincide with the theoretical analysis.     

Finite-time outer-synchronization for complex networks with Markov jump topology via hybrid control and its application to image encryption

This paper investigates the problem of finite-time outer-synchronization for discrete-time complex networks with Markov jump topology in the presence of communication delays and possible information losses and its application to image encryption. A hybrid control, which is subject to both stochastic jumps and deterministic switches, is proposed to realize finite-time and stochastic outer-synchronization for the concerned networks. By utilizing a stochastic Lyapunov functional combined with the average dwell-time method, sufficient conditions are found such that the synchronization error dynamical system is stochastically stable in finite-time. Two numerical examples are presented to illustrate the effectiveness of the proposed method. Finally, the complex network consists of four coupled Lorenz systems are utilized to generate chaotic sequences and a new chaotic image cryptosystem is constructed to transmit encrypted images based on the synchronized drive-response complex networks. Experiments are conducted by using numerical simulation, and the security is analyzed in terms of key space, key sensitivity, histogram distributions, correlation coefficients, information entropy and differential attack measures. The experimental results show that the proposed chaotic image cryptosystem has the advantages of high security against some classical attacks.     

Internet of health things encryption via master-slave synchronization for stochastic quaternion-valued neural networks

This paper investigates the problem of master-slave synchronization of stochastic quaternion-valued neural networks (SQVNNs) with mixed time-varying delays. A linear feedback controller is developed to explore the global synchronization of the proposed system by utilizing the complete information of the time-delay state. Sufficient conditions for synchronization of the proposed model are derived by constructing appropriate Lyapunov–Krasovskii functional by applying the master-slave synchronization method of master-slave and some integral inequality techniques. Finally, a corresponding numerical simulation is presented to demonstrate the accuracy of the theoretical results. This paper introduces a unique and efficient image encryption algorithm based on SQVNNs. This technique utilizes the solution set of SQVNNs to generate the high-level randomness secret keys to encrypt the source image. Finally, we conclude that the algorithm yields a source image cipher with excellent diffusion and confusion properties. A few test clinical images are utilized to show the validity of the proposed method. Several performance analyses show that the proposed algorithm for image encryption gives an efficient and secure way to deal with the Internet of Health Things (IoHT).     

Fault-tolerant tracking control based on reinforcement learning with application to a steer-by-wire system

In this paper, a novel complete model-free integral reinforcement learning (CMFIRL) algorithm based fault tolerant control scheme is proposed to solve the tracking problem of steer-by-wire (SBW) system. We begin with the recognition that the reference errors can eventually converge to zero based on the command generator model. Then an augmented tracking system is constructed with a corresponding performance index which is considered as a type of actuator failure. By using the reinforcement learning (RL) technique, three novel online update strategies are respectively developed to cope with the following three cases, i.e., model-based, partially model-free, and completely model-free. Especially, the RL algorithm for the complete model-free case eliminates the constraints of requiring the known system dynamics in fault-tolerant tracking controlling. The system stability and the convergence of the CMFIRL iteration algorithm are also rigorously proved. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.     

一种基于外部密钥和密文反馈的混沌密码新算法

提出了一种基于逐段线性混沌系统的图像加密算法。通过对外部密钥的映射,分别产生系统的初值和参数值,根据图像大小经16个逐段线性映射迭代出足够的密钥流,并引入密文反馈机制,对图像像素值逐个进行多轮异或加密。实验表明,这种加密算法使密文对明文和密钥都充分敏感,加密图像像素值具有类随机均匀分布特性。而且算法具有密钥空间大、加密速度快的优越性。     

Synchronization for chaotic systems via mixed-objective dynamic output feedback robust model predictive control

This paper focuses on mixed-objective dynamic output feedback robust model predictive control (OFRMPC) for the synchronization of two identical discrete-time chaotic systems with polytopic uncertainties, energy bounded disturbances, and input constraint. Using active control strategy, the chaos synchronization is transformed into standard dynamic OFRMPC scenarios tractable through receding horizon min–max optimization. Utilizing the notion of quadratic boundedness, the augmented closed-loop stability is further characterized. Then, the concepts of mixed performance criteria are firstly incorporated into the dynamic OFRMPC scheme to guarantee both the robust stability and the disturbance attenuation ability while preserving better dynamical behaviors. Necessary and/or sufficient conditions for desired mixed-objective dynamic OFRMPC are formulated involving linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the theoretical results.     

Command filtered adaptive neural network synchronization control of fractional-order chaotic systems subject to unknown dead zones

Command filters are essential for alleviating the inherent computational complexity (ICC) of the standard backstepping control method. This paper addresses the synchronization control scheme for an uncertain fractional-order chaotic system (FOCS) subject to unknown dead zone input (DZI) based on a fractional-order command filter (FCF). A virtual control function (VCF) and its fractional-order derivative are approximated by the output of the FCF. In order to handle filtering errors and obtain good control performance, an error compensation mechanism (ECM) is developed. A radial basis function neural network (RBFNN) is introduced to relax the requirement of the uncertain function must be linear in the standard backstepping control method. The construction of a VCF in each step satisfies the Lyapunov function to ensure the stability of the corresponding subsystem. By using the bounded information to cope with the unknown DZI, the stability of the synchronization error system is guaranteed. Finally, simulation results verify the effectiveness of our methods.     

Chaotic synchronization based on neural filter

Because of the high sensitivity of chaotic systems to their initial conditions, synchronization of chaotic systems with uncertain parameters has been a challenging problem especially in noisy environment. Since synchronization of the transmitter and receiver systems involves recursive estimation, recursive nonlinear filters are called for and the extended Kalman (EKF) filter and unscented Kalman (UKF) filter have been applied. However, such suboptimal filters incur high synchronization errors and provide no capacity for uncertain environment, which motivated the use of the neural filter for chaotic synchronization in this paper. The neural filter, which is a recurrent neural network, can approximate the minimum-variance to any degree. Furthermore, the neural filter can adapt to a uncertain environment without online filter weight adjustment, which is computationally efficient. Numerical experiments show that the chaotic synchronization scheme based on the neural filter outperforms those based on EKF and UKF by a large margin.     

基于Lyapunov方法Lorenz混沌系统自适应同步方法

对于具有不确定参数的Lorenz混沌系统，通过参数调节和自适应技术讨论了两个同结构Lorenz混沌系统的同步问题。自适应控制器和参数调节律均由Lyapunov稳定行理论来确定。数字仿真表明了该方法的有效性和实用性。     

基于盲源分离理论的图像加密算法概述

随着盲源分离理论的日渐成熟,其应用领域也越来越广泛,尤其在图像加密领域中,提出了基于独立分量分析(ICA)、基于非负矩阵分解(NMF)的加密新方法,以及盲源分离加密与混沌结合的加密方法等。本子将对以上基于盲源分离理论的加密新方法进行具体阐述。     

Adaptive synchronization of multi-agent systems via variable impulsive control

This paper mainly focuses on the adaptive synchronization problem of multi-agent systems via distributed impulsive control method. Different from the existing investigations of impulsive synchronization with fixed time impulsive inputs, the proposed distributed variable impulsive protocol allows that the impulsive inputs are chosen within a time period (namely impulsive time window) which can be described by the distances of the left (right) endpoints or the centers between two adjacent impulsive time windows. Obviously, this kind of flexible control scheme is more effective in practical systems (especially for the complex environment with physical restrictions). Moreover, the proposed adaptive control technique is helpful to solve the problem with uncertain system parameters. By means of Lyapunov stability theory, impulsive differential equations and adaptive control technique, three sufficient impulsive consensus conditions are given to realize the synchronization of a class of multi-agent nonlinear systems. Finally, two numerical simulations are provided to illustrate the validity of the theoretical analysis.     

混沌通讯加密卡的软件设计

本文概要介绍了混沌通讯加密卡的硬件原理,重点阐述混沌通讯加密卡的软件设计方案。     

A symmetric image encryption scheme based on combination of nonlinear chaotic maps

During the recent years several chaotic image encryption algorithms have been proposed, but most of them encountered some drawbacks such as small key space, low speed, lack of robustness and low security. In this paper, we have proposed an image algorithm based on the combination of a one-dimensional polynomial chaotic map and a piecewise nonlinear chaotic map. Theoretical analysis and computer simulations, both confirm that the new algorithm possesses high security, robust fast encryption speed for practical image encryption and solves the problem of small key space.     

Finite-time inter-layer projective synchronization of Caputo fractional-order two-layer networks by sliding mode control

Finite-time inter-layer projective synchronization (FIPS) of Caputo fractional-order two-layer networks (FTN) based on sliding mode control (SMC) technique is investigated in this article. Firstly, in order to realize the FIPS of FTN, a fractional-order integral sliding mode surface (SMS) is established. Then, through the theory of SMC, we design a sliding mode controller (SMCr) to ensure the appearance of sliding mode motion. According to the fractional Lyapunov direct method, the trajectories of the system are driven to the proposed SMS, and some novel sufficient conditions for FIPS of FTN are derived. Furthermore, as two special cases of FIPS, finite-time inter-layer synchronization and finite-time inter-layer anti-synchronization for the FTN are studied. Finally, this paper takes the fractional-order chaotic Lü’s system and the fractional-order chaotic Chen’s system as the isolated node of the first layer system and the second layer system, respectively. And the numerical simulations are given to demonstrate the feasibility and validity of the proposed theoretical results.     

Dynamic output feedback sliding mode control for spacecraft hovering without velocity measurements

In consideration of target angular velocity uncertainty and external disturbance, a modified dynamic output feedback sliding mode control (DOFSMC) method is proposed for spacecraft autonomous hovering system without velocity measurements. As a stepping-stone, an additional dynamic compensator is introduced into the design of sliding surface, then an augmented system is reconstructed with the system uncertainty and external disturbance. Based on the linear matrix inequality (LMI), a sufficient condition is given, which guarantees the disturbance attenuation performance of sliding mode dynamics. By introducing an auxiliary variable, a modified version of adaptive sliding mode control (ASMC) law is designed, and the finite-time stability of sliding variable is established by the Lyapunov stability theory. Compared with other results, the proposed method is less conservative and can decrease the generated control input force significantly. Finally, two simulation examples are performed to validate the effectiveness of the proposed method.     

Application of matrix semi-tensor product in chaotic image encryption

This paper proposes a new image encryption method based on matrix semi-tensor product theory. Using Hyperchaotic Lorenz system to generate chaotic sequences, and then using this chaotic sequence to generate two fixed scrambling matrices. The plain image is scrambled by chaotic positioning sort scrambled method. Analogous to a chemical reaction, the plain image scrambled image is one of the reactant, then add a matrix which is related to the plain image information and extracted from the chaotic sequence (this matrix can be differ in size from the plain image matrix, different matrices can be intercepted and generated according to different plain image). This matrix is scrambled as another reactant, Apply the method of semi-tensor product to carry on the reaction (diffusion), finally get the product (encryption image). This method breaks the shackles of the traditional matrix operation and makes the reaction matrix have more forms. Compared with other experimental results, the proposed algorithm is more secure and available.