Impulsive synchronization of time-varying dynamical network

Synchronization of time-varying dynamical network is investigated via impulsive control. Based on the Lyapunov function method and stability theory of impulsive differential equation, a synchronization criterion with respect to the system parameters and the impulsive gains and intervals is analytically derived. Further, an adaptive strategy is introduced for designing unified impulsive controllers, with a corresponding synchronization criterion derived. In this proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is provided and evaluated. The derived theoretical results are illustrated to be effective by several numerical examples.     

Chaos of time-varying discrete dynamical systems

This paper is concerned with chaos of time-varying (i.e. non-autonomous) discrete systems in metric spaces. Some basic concepts are introduced for general time-varying systems, including periodic point, coupled-expansion for transitive matrix, uniformly topological equiconjugacy, and three definitions of chaos, i.e. chaos in the sense of Devaney and Wiggins, respectively, and in a strong sense of Li–Yorke. An interesting observation is that a finite-dimensional linear time-varying system can be chaotic in the original sense of Li–Yorke, but cannot have chaos in the strong sense of Li–Yorke, nor in the sense of Devaney in a set containing infinitely many points, and nor in the sense of Wiggins in a set starting from which all the orbits are bounded. A criterion of chaos in the original sense of Li–Yorke is established for finite-dimensional linear time-varying systems. Some basic properties of topological conjugacy are discussed. In particular, it is shown that topological conjugacy alone cannot guarantee two topologically conjugate time-varying systems to have the same topological properties in general. In addition, a criterion of chaos induced by strict coupled-expansion for a certain irreducible transitive matrix is established, under which the corresponding nonlinear system is proved chaotic in the strong sense of Li–Yorke. Two illustrative examples are finally provided with computer simulations for illustration.     

Intelligent control of chaos using linear feedback controller and neural network identifier

A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems, equivalent discrete-time systems are constructed by using the Poincare map concept. Two discrete-time systems and one continuous-time system are tested as examples for simulation and the results show good functionality of the proposed method. It can be concluded that the chaos in systems with unknown dynamics may be eliminated by the presented intelligent control system based on pole placement and neural network.     

Chaos control of chaotic dynamical systems using backstepping design

This work presents chaos control of chaotic dynamical systems by using backstepping design method. This technique is applied to achieve chaos control for each of the dynamical systems Lorenz, Chen and Lü systems. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical simulations are shown to verify the results.     

Neural network hybrid adaptive control for nonlinear uncertain impulsive dynamical systems

A neural network hybrid adaptive control framework for nonlinear uncertain hybrid dynamical systems is developed. The proposed hybrid adaptive control framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop hybrid system; that is, asymptotic stability with respect to part of the closed-loop system states associated with the hybrid plant states. A numerical example is provided to demonstrate the efficacy of the proposed hybrid adaptive stabilization approach.     

Robust stabilization of uncertain linear dynamical systems with time-varying delay

In this paper, the problem of the robust stabilization for a class of uncertain linear dynamical systems with time-varying delay is considered. By making use of an algebraic Riccati equation, we derive some sufficient conditions for robust stability of time-varying delay dynamical systems with unstructured or structured uncertainties. In our approach, the only restriction on the delay functionh(t) is the knowledge of its upper boundh ^–. Some analytical methods are employed to investigate these stability conditions. Since these conditions are independent of the delay, our results are also applicable to systems with perturbed time delay. Finally, a numerical example is given to illustrate the use of the sufficient conditions developed in this paper.     

Modelling framework for artificial hybrid dynamical systems

Many current industry branches use hybrid approaches to solve complex application problems. Over the last decades, different tools for the simulation of such hybrid systems (e.g. Hysdel and YAMLIP) as well as the identification of hybrid systems (e.g. HIT, MLP and OAF NN) have been developed. The framework presented in this work facilitates the integration of artificial feed-forward neural networks in the modelling process of hybrid dynamical systems (HDS). Additionally, the framework provides a structured language for characterising these feed-forward networks itself. Therefore, an interdisciplinary exchange in the field of neural networks and its integration into hybrid dynamical systems is enabled. Focusing on hybrid systems with autonomous events, two different approaches, namely the artificial hybrid model and the artificial hybrid dynamics, are introduced. Challenges of the modelling process of HDS are reflected and advantages as well as disadvantages are discussed. The case study includes two common examples of HDS and analyses the simulation results and examines limitations of the modelling framework.     

Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

In this paper, a new method to synchronize two identical chaotic recurrent neural networks is proposed. Using the drive-response concept, a nonlinear feedback control law is derived to achieve the state synchronization of the two identical chaotic neural networks. Furthermore, based on the Lyapunov method, a delay independent sufficient synchronization condition in terms of linear matrix inequality (LMI) is obtained. A numerical example with graphical illustrations is given to illuminate the presented synchronization scheme.     

Establishing criteria to ensure successful feedforward artificial neural network modelling of mechanical systems

The emulation of mechanical systems is a popular application of artificial neural networks in engineering. This paper examines general principles of modelling mechanical systems by feedforward artificial neural networks (FFANNs). The slow convergence issue associated with the highly parallel and redundant structure of FFANN systems is addressed by formulating criteria for constraining network parameters so that FFANNs may be reliably applied to mechanics problems. The existence of the FFANN mechanical model and its stability during construction, with respect to the error in the data, are analyzed. Also, a class of differential equations is analyzed for use with Tikhonov regularization. It is shown that the use of Tikhonov regularization can aid in FFANN data-driven construction with a priori mathematical models of varying degrees of physical fidelity. Criteria to ensure successful FFANN application from an engineering perspective are established.     

基于递归型神经网络动力学求解时变凸二次规划

为了在线求解时变凸二次规划问题,实现误差精度更高、求解时间更短和收敛速度更快的目标。本文采用了求解问题更快的时变网络设计参数,选择了有限时间可以收敛的Sign-bi-power激活函数,构造了一种改进的归零神经网络动力学模型。其后,分析了模型的稳定性和收敛性,得到其解能够在有限时间内收敛。最后,在仿真算例中,与传统的梯度神经网络和归零神经网络模型相比,所提模型具有更高的误差精度、更短的求解时间和更快的收敛速度,优于前两种网络模型。     

Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion

In this paper, a new complex-valued recurrent neural network (CVRNN) called complex-valued Zhang neural network (CVZNN) is proposed and simulated to solve the complex-valued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued time-varying matrix in an error-free manner. Moreover, by exploiting the design parameter γ>1, superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter γ involved (i.e., the situation with γ=1). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion.     

Periodic solution to BAM-type Cohen-Grossberg neural network with time-varying delays

By using the continuation theorem of Mawhin’s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.     

Optimal control of parabolic systems with time-varying lags

Various optimal control problems for linear parabolic systemswith time-varying lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwart's, the representation of the optimalfeedback control is given.     

Sensitivity of time-varying,linear optimal control systems

This paper analyzes the following fundamental question: In what precise sense, if any, is the closed-loop realization of an optimal control system less sensitive to parameter variations than the nominally equivalent open-loop system? This question is answered for time-varying, linear optimal control systems. It is shown that there is a closed-loop sensitivity reduction in terms of an inequality involving a particular integral-square of the first-order variation of the state due to first-order variations of plant parameters.     

Horseshoe in a model of artificial neural network

In this paper, we study a three-dimensional general model of artificial neural network (ANN). To confirm the chaotic behavior in this neural network demonstrated in numerical studies, we consider a cross-section properly chosen for the attractor obtained and study the dynamics of the corresponding Poincaré map, and rigorously verify the existence of horseshoe by computer-assisted verification arguments.     

Adaptive scheme for time-varying anticipating synchronization of certain or uncertain chaotic dynamical systems

In this paper, a new type of anticipating synchronization, called time-varying anticipating synchronization, is defined firstly. Then novel adaptive schemes for time-varying anticipating synchronization of certain or uncertain chaotic dynamical systems are designed based on the Lyapunov function and invariance principle. The update gain of coupling strength can be automatically adapted to a suitable strength depending on the initial values and can be properly chosen to adjust the speed of achieving synchronization, so these schemes are analytical and simple to implement in practice. A classical chaotic dynamical system is used to demonstrate the effectiveness of the proposed adaptive schemes with or without parameter uncertainties.     

Projective synchronization of time-varying delayed neural network with adaptive scaling factors

In this work, the projective synchronization between two continuous time delayed neural systems with time varying delay is investigated. A sufficient condition for synchronization for the coupled systems with modulated delay is presented analytically with the help of the Krasovskii–Lyapunov approach. The effect of adaptive scaling factors on synchronization are also studied in details. Numerical simulations verify the effectiveness of the analytic results.     

Global synchronization of weighted cellular neural network with time-varying coupling delays

New sufficient conditions are derived to guarantee the global synchronization of the weighted cellular neural network with multiple time delays. Based on Lyapunov theory, this paper proposes an adaptive feedback controlling method to identify the exact topology of a rather general weighted cellular neural network system with time-varying delays and then considers the synchronization of the neural network with different nodes dynamics. The parameters in this paper are very few and experiments show that the methods presented in this paper are of high application in global synchronization.