Scaling Function Matrix Research Articles

Adaptive fault-tolerant control for the ascent phase of hypersonic vehicle with time-varying full state constraints

In this paper, a novel attitude adaptive fault-tolerant control (FTC) scheme is presented for the ascent phase of hypersonic vehicle (HSV) subject to pneumatic-propulsion coupling and time-varying full state constraints, which are unique to the ascent phase of HSV and are caused by the integrated design of fuselage engine and power system switching. Compared with some existing methods for time-varying constraints, the proposed control method contains a constrained function so that constraints can be incorporated directly into the state, which asymmetric and time-varying state constraints can be handled without feasibility conditions. Moreover, by designing a time-varying scaling function matrix to transform the tracking error, the proposed method enables the practical tracking control to be achieved without any switching for a multi-input multi-output (MIMO) pure-feedback system which is transformed from the ascent phase model of HSV. Besides, to incorporate constraints into the state, an adaptive fault estimation filter is designed to estimate unknown faults and disturbances. It is proved that the proposed FTC scheme can guarantee that the closed-loop control system is stable and the time-varying state constraints are satisfied. Finally, simulation results are provided to illustrate the effectiveness of the proposed FTC scheme.

Function Projective Synchronization between Two Discrete-Time Hyperchaotic Systems Using Backstepping Method

We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the backstepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

A new synchronisation method of fractional-order chaotic systems with distinct orders and dimensions and its application in secure communication

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed.

An application of adaptive synchronization of uncertain chaotic system in secure communication systems

ABSTRACT Chaotic secure communication via synchronization of chaotic systems has attracted increasing attention in recent years. This note aims to introduce the function projective synchronization (FPS) of coupled fractional-order (FO) complex chaotic Lü system in the master-slave system formalism up to the desired scaling function matrix in the presence of bounded model uncertainties. An efficient chaotic secure communication scheme is proposed using the chaotic masking approach. In order to increase the unpredictability of the information signal, the transmitted signals to the channel are considered as the FO derivative of the product of the information signal and the states of the chaotic system. At the receiver side, by employing the Lyapunov stability theorem, an appropriate adaptive FO control law is derived to synchronize the master and slave systems. After the robust synchronization is achieved, the information signal can be recovered accurately with high speed in the transient response. Finally, to verify the effectiveness of the theoretical results, two numerical simulations are performed and some comparisons based on the adaptation parameter of the control law are provided.

A novel dual memristor hyperchaotic system and its application for secure communication based on three‐fold function projection synchronization

AbstractA novel simplest four‐dimensional hyperchaotic system with dual memristors is designed by using a charge‐controlled memristor and a generalized voltage‐controlled memristor. Based on the conventional dynamic analysis method and MATLAB simulation software, the dynamic characteristics of the dual memristor hyperchaotic system such as Lyapunov exponent spectrum, phase diagram, and bifurcation diagram are studied. The novel system is found to exhibit singular nonlinear phenomena, such as limit cycle, state transition and multiple scroll attractor with certain parameter values. Being different from most known chaotic systems, which contain only two isolated unstable equilibrium points, the novel system has an infinite number of unstable equilibriums points and a larger Lyapunov exponent. What is more, the three‐fold function projection synchronization of the dual memristor hyperchaotic system and its application for secure communication is studied. Based on Lyapunov stabilization theory and adaptive sliding mode control method, three driving systems and three response systems are synchronized according to the corresponding scaling function matrix, respectively. In the secure communication system, the message signal is separated into three parts loaded in the different drive systems with different initial conditions to increase the reliability. The corresponding numerical simulations demonstrate the effectiveness of the results obtained.

Cluster-modified function projective synchronisation of complex networks with asymmetric coupling

This paper investigates the cluster-modified function projective synchronisation (CMFPS) of a generalised linearly coupled network with asymmetric coupling and nonidentical dynamical nodes. A novel synchronisation scheme is proposed to achieve CMFPS in community networks. We use adaptive control method to derive CMFPS criteria based on Lyapunov stability theory. Each cluster of networks is synchronised with target system by state transformation with scaling function matrix. Numerical simulation results are presented finally to illustrate the effectiveness of this method.

Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.

Function Projective Lag Synchronization of Chaotic Systems with Certain Parameters via Adaptive-Impulsive Control

A new method is presented to study the function projective lag synchronization (FPLS) of chaotic systems via adaptiveimpulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.

Modified function projective synchronization of complex dynamical networks with mixed time-varying and asymmetric coupling delays via new hybrid pinning adaptive control

This paper investigates modified function projective synchronization (MFPS) for complex dynamical networks with mixed time-varying and hybrid asymmetric coupling delays, which is composed of state coupling, time-varying delay coupling and distributed time-varying delay coupling. In contrast to previous results, the coupling configuration matrix needs not be symmetric or irreducible. The MFPS of delayed complex dynamical networks is considered via either hybrid control or hybrid pinning control with nonlinear and adaptive linear feedback control, which contains error linear term, time-varying delay error linear term and distributed time-varying delay error linear term. Based on Lyapunov stability theory, adaptive control technique, the parameter update law and the technique of dealing with some integral terms, we will show that control may be used to manipulate the scaling functions matrix such that the drive system and response networks could be synchronized up to the desired scaling function matrix. Numerical examples are given to demonstrate the effectiveness of the proposed method. The results in this article generalize and improve the corresponding results of the recent works.

Adaptive Modified Function Projective Lag Synchronization of Memristor-Based Five-Order Chaotic Circuit Systems

The modified function projective lag synchronization of the memristor-based five-order chaotic circuit system with unknown bounded disturbances is investigated. Based on the LMI approach and Lyapunov stability theorem, an adaptive control law is established to make the states of two different memristor-based five-order chaotic circuit systems asymptotically synchronized up to a desired scaling function matrix, while the parameter controlling strength update law is designed to estimate the parameters well. Finally, the simulation is put forward to demonstrate the correctness and effectiveness of the proposed methods. The control method involved is simple and practical.

Modified function projective synchronization between two different complex networks with delayed couplings and delayed nodes of different dimensions

In this paper, to deal with the problem of modified function projective synchronization (MFPS) between two different networks with delayed couplings and delayed nodes of different dimensions, a hybrid control scheme combining adaptive control and nonlinear control is proposed. First, a more realistic drive-response complex network model is constructed by introducing double delays. Then, we design hybrid feedback controllers to synchronize up the drive and response networks of different dimensions to a scaling function matrix. Based on Lyapunov stability theory and the linear matrix inequality (LMI), we rigorously prove that the MFPS between the proposed drive-response networks can be achieved and meanwhile some sufficient conditions are derived by adopting an appropriate Lyapunov–Krasovskii energy function. Noteably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method.

A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities

In this paper, a modified generalized function projective synchronization scheme for a class of master–slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.

Partial switched modified function projective synchronization of unknown complex nonlinear systems

Many studies on the switched modified function projective synchronization of nonlinear real dynamic systems have been carried out, whereas the switched modified function projective synchronization of chaotic complex systems has not been studied extensively. In this paper, the concept of the partial switched modified function projective synchronization of complex nonlinear systems with fully unknown parameters is proposed. Partial switched synchronization of chaotic systems means that the state variables of the drive system synchronize with partial different state variables of the response system. Based on the parameter modulation and the adaptive control technique, the adaptive control laws and the parameter update laws are derived to make the states of two different complex nonlinear systems asymptotically synchronized up to a desired scaling function matrix. The given scaling function can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Finally, numerical simulations are performed to verify the feasibility and effectiveness of the proposed controllers and identifiers.

Complex function projective synchronization of general networked chaotic systems by using complex adaptive fuzzy logic

This paper is concerned with the problem of complex function projective synchronization for uncertain networked chaotic complex systems. Based on Lyapunov stability, an adaptive control method is proposed for complex modified projective synchronization, which guarantees that the general drive-response networked chaotic complex systems are synchronized up to a complex scaling function matrix. Moreover, a complex fuzzy logic-based observer is designed to compensate for the model uncertainties and the external disturbances that exist in response networks, without prior information about uncertain factors. Numerical simulations are presented to demonstrate the effectiveness of the proposed method.

Modified function projective lag synchronization of hyperchaotic complex systems with parameter perturbations and external perturbations

In this paper, a novel synchronization method of modified function projective lag synchronizations (MFPLS) between identical and nonidentical hyperchaotic complex nonlinear systems with parameter perturbations and external perturbations is proposed. In the method, the states of two hyperchaotic complex systems with parameter perturbations and external perturbations are asymptotically lag synchronized up to a desired scaling function matrix, and all the perturbations in the parameters asymptotically converge to zero. Base on the Lyapunov stability theory, the adaptive controller and updating laws of parameter perturbations are designed to achieve MFPLS between the drive and response systems. Theoretically the proof that the drive and response system will asymptotically lag synchronization and numerical simulations verify the feasibility and effectiveness of the proposed scheme.

Function projective lag synchronization of fractional-order chaotic systems

Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.

Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

The Construction of the SGW-Based Bar-Beam Elements

PsdVoigt2 function was used to fit SGW function and a series of bar beam elements based on the theory of SGW and wavelet finite element were constructed. Traditional finite element polynomial interpolation was replaced by the SGW scaling function and transformation matrix was utilized to transform wavelet interpolation coefficients to physical space. Thereby the shape function and element were constructed. The precision of a series of bar beam elements constructed with the SGW scale function as the interpolation function were verified by the calculation cases. The calculation results showed that the precision of the SGW-based element constructed was higher in calculating the deformation and strain. And the SGW-based bar beam element constructed enriched the element library of wavelet-finite element method.

Hybrid modified function projective synchronization of two different dimensional complex nonlinear systems with parameters identification

In this article, a novel synchronization scheme is proposed to achieve hybrid modified function projective synchronization (HMFPS) in two different dimensional complex nonlinear systems with fully unknown parameters. In the complex space, the response system are asymptotically synchronized up to the different order’s drive system by the state transformation with a scaling function matrix, and all of unknown parameters in both drive and response systems are achieved to be identified. Based on the Lyapunov stability theory, an adaptive controller and updated laws of parameters are developed. Respectively on the ways of increased order and reduced order, the corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Adaptive modified function projective lag synchronization of hyperchaotic complex systems with fully uncertain parameters

In this article, a novel synchronization scheme, modified function projective lag synchronization (MFPLS), between identical and nonidentical hyperchaotic complex systems with fully uncertain parameters, is proposed. In the proposed general method, the states of two hyperchaotic complex systems with unknown parameters are asymptotically synchronized up to a desired scaling function matrix with time delay, and all of the unknown parameters are identified. The adaptive controller and laws of parameters are designed to achieve MFPLS between the drive and response systems. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.