FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

The global finite-time synchronization control of a type of fourth-order hyperchaotic systems with intersecting nonlinearities was studied. Firstly, the matrix form of this kind of hyperchaotic system was given to construct the master-slave synchronization models based on the generalized linear state error feedback controller. Then, the finite-time synchronization problem was equivalent to the finite-time stability of the error system originating from the master-slave hyperchaotic systems. The global finite-time stability of the error system was proven by the finite-time stability theory, further obtaining the criterion for global finite-time synchronization and the synchronization time estimation in mathematical formula. Subsequently, the theoretical results were applied to the well-known hyperchaotic Lorenz-stenflo system. The finite-time synchronization criteria for hyperchaotic Lorenz-stenflo systems were further proven by using optimization technology, and the corresponding synchronization times were estimated. Finally, the simulation was conducted by the MATLAB software, showing that two hyperchaotic Lorenz-stenflo systems could synchronize in a finite time.

This paper studies a linear feedback synchronization scheme for the chaotic Lorenz-Stenflo systems. Some sufficient algebraic criteria for global chaos synchronization of the master and slave Lorenz-Stenflo systems via linear state error feedback control are rigorously proven by means of Lyapunov stability theory. The obtained criteria are further optimized to improve their sharpness. The numerical examples verify the effectiveness of these criteria.

This paper investigates the global chaos synchronization for master-slave modified Chuapsilas circuit systems coupled by linear state error feedback control. Some sufficient global synchronization criteria are derived in the algebraic inequality form. The numerical examples illustrate the effectiveness of the obtained criteria.

This paper is concerned with master‐slave synchronization of chaotic Φ6 Duffing oscillators by using linear state error feedback control. Compared with some existing methods and results, this paper estimates the bound of the first trajectory (variable) of the controlled slave system and uses this bound to derive synchronization criteria for two chaotic Φ6 Duffing oscillators. The effectiveness of synchronization criteria is illustrated by three simulation examples.

Optimized linear active disturbance rejection control for pneumatic servo systems via least squares support vector machine

Chaotic synchronization by the intermittent feedback method

In this paper, the projective synchronization problem of nonautonomous neural networks with time delay and Caputo derivative is researched. First, by introducing time delay and variable coefficient into the known neural network model, the neural network that can more accurately describe the interaction between neurons is given. Second, based on the improved neural network model, two global synchronization schemes are achieved, respectively. Finally, by constructing two novel Lyapunov functions and utilizing the properties of delay fractional-order differential inequalities, the asymptotic stability of the zero equilibrium point of the error system obtained from the master–slave systems is proved by some new developing analysis methods, respectively, and some criteria for global projective synchronization of delayed nonautonomous neural networks with Caputo derivatives are obtained, respectively, under two new synchronous controllers. In addition, the correctness of the theoretical results obtained in this paper is verified by some numerical simulation.

Global synchronization in general complex delayed dynamical networks and its applications

This paper presents a framework for finite-time global synchronization of Markovian jump complex networks (MJCNs) with partially unknown transition rates, time-delays and stochastic noises. Several criteria for finite-time global synchronization are given by using the stochastic analysis techniques and matrix theory. These criteria provide a feasible approach to design linear feedback controller and to compute finite-time of global synchronization for the addressed MJCNs. Four numerical examples are given to demonstrate the effectiveness of the theoretical results.

Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality

Chaos synchronization of an energy resource system based on linear control

A linear output feedback controller is developed for trajectory tracking problems defined on a modified version of Chua's circuit. The circuit modification considers the introduction of a suitable external control input channel guided by a) the induction of the flatness property on a measurable output signal of the circuit and b) the physical viability of the control input. A linear active disturbance rejection control, based on a high gain linear disturbance observer, is implemented on a laboratory prototype. We show that the state-dependent disturbance can be approximately, but arbitrarily closely, estimated through a linear, high-gain, observer, called a Generalized Proportional Integral (GPI) observer, which contains a linear combination of a sufficient number of extra iterated integrals of the output estimation error. Experimental results are presented in the output reference trajectory tracking of a signal generated by an unrelated chaotic system of the Lorenz type. Laboratory experiments illustrate the proposed linear methodology for effectively controlling chaos.

A linear output feedback controller is developed for trajectory tracking problems defined on a modified version of Chua's circuit. The circuit modification considers the introduction of a flat input, i.e. a suitable external control input channel guided by (a) the induction of the flatness property on a measurable output signal of the circuit and (b) the physical viability of the control input. A linear active disturbance rejection control based on a high-gain linear disturbance observer, is implemented on a laboratory prototype. We show that the state-dependent disturbance can be approximately, but arbitrarily closely, estimated through a linear high-gain observer, called a generalised proportional integral (GPI) observer, which contains a linear combination of a sufficient number of extra iterated integrals of the output estimation error. Experimental results are presented in the output reference trajectory tracking of a signal generated by an unrelated chaotic system of the Lorenz type. Laboratory experiments illustrate the proposed linear methodology for effectively controlling chaos.

This paper investigates the global synchronization method of two identical systems and two different chaotic systems. The proposed method is effective and convenient to synchronize two identical systems and two different chaotic systems by using nonlinear control functions. The method has been applied successfully to make two identical four-scroll attractor and also two different chaotic systems; four-scroll attractor and Lorenz system globally synchronized. Numerical simulations are given to validate the proposed synchronization methods. Key words: Chaotic system, global synchronization, four-scroll attractor,Lorenz system, Lyapunov function.

This article describes the design of a linear observer–linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in the case of nonlinear, multivariable, nonholonomic underactuated mobile manipulators. The proposed linear feedback scheme is based on the use of a classical linear feedback controller and suitably extended, high-gain, linear Generalized Proportional Integral (GPI) observers, thus aiding the linear feedback controllers to provide an accurate simultaneous estimation of each flat output associated phase variables and of the exogenous and perturbation inputs. This information is used in the proposed feedback controller in (a) approximate, yet close, cancelations, as lumped unstructured time-varying terms, of the influence of the highly coupled nonlinearities, and (b) the devising of proper linear output feedback control laws based on the approximate estimates of the string of phase variables associated with the flat outputs simultaneously provided by the disturbance observers. Simulations reveal the effectiveness of the proposed approach.