Robust Finite-time Synchronization Research Articles

A fractional-order quantum neural network: dynamics, finite-time synchronization

A model of fractional-order quantum cellular neural network (FoQCNN) by using fractional-order quantum-dot cellular automata (QCA) is constructed and its dynamics are analyzed. Then, a robust finite-time synchronization scheme using terminal sliding mode control (SMC) technique is proposed. And then, taking the perturbed FoQCNN model with uncertainties and external disturbances as an example, the results are simulated which present the proposed scheme is effective. It has robust synchronization performance and good anti-interference ability, which provides a theoretical basis for the application of neural network in security.

Robust Finite-Time Synchronization of Recurrent Neural Networks via Saturated Control

This brief studies the finite-time synchronization of a class of recurrent neural networks, where the dual effects of the saturation structure and uncertain factors on the system are fully considered. By designing different classes of saturated controllers, some sufficient conditions guaranteeing robust finite-time synchronization are proposed, where the estimations of the settling-time and the domain of attraction are obtained. In particular, in the framework of saturation structure, the designed controller can be improved a simpler form to further acquire globally robust finite-time synchronization. Finally, a numerical example is demonstrated to verify the presented results.

Finite-time synchronization and [formula omitted] synchronization of coupled complex-valued memristive neural networks with and without parameter uncertainty

In this paper, finite-time synchronization and H∞ synchronization of coupled complex-valued memristive neural networks (CCVMNNs) with or without parameter uncertainty are analyzed. First, a finite-time synchronization (FTS) condition is presented for CCVMNNs by means of deploying Lyapunov stability theory and developing suitable controllers. Then, we utilize the similar method to derive a criterion of robust finite-time synchronization (RFTS) for the proposed CCVMNNs with uncertain parameter. Furthermore, we establish some criteria for the sake of ensuring that the considered network can reach finite-time H∞ synchronization and robust finite-time H∞ synchronization. At last, two numerical examples with simulations demonstrate the validity of the acquired results.

Non-separation method-based robust finite-time synchronization of uncertain fractional-order quaternion-valued neural networks

In this paper, robust finite-time synchronization (F-TS) issue is addressed for a class of uncertain fractional-order quaternion-valued neural networks by employing non-separation method instead of separation method. First, a general fractional differential inequality is developed to provide new insight into the research about finite-time stability and synchronization of fractional-order systems. Next, quaternion-valued feedback controller and quaternion-valued adaptive controller are designed. On the basis of the newly developed inequality, quaternion inequality techniques, together with the properties of fractional calculus and reduction to absurdity, some easily-verified algebraic criteria for robust F-TS are established, and the settling time for robust F-TS is explicitly reckoned, which depends on not only the controller parameters but also the initial values and order of the considered systems. Eventually, numerical results are provided to substantiate our robust F-TS criteria.

Non-fragile robust finite-time synchronization for fractional-order discontinuous complex networks with multi-weights and uncertain couplings under asynchronous switching

This paper focus on the global robust non-fragile finite-time synchronization issue for fractional-order complex networks with multi-weights and uncertain couplings under asynchronous switching topology, where nonlinear dynamic nodes are discontinuous and non-decreasing. Firstly, the non-fragile controller with switching gains is designed. Secondly, under the fractional Filippov differential inclusion framework and the network topologies with no-delayed and delayed couplings, by adopting multiple Lur’e Postnikov-type Lyapunov functional, nonsmooth analysis method and the average dwell time technique, the global robust non-fragile finite-time synchronization conditions are achieved in terms of linear matrix inequalities (LMIs), respectively. Finally, the validity of the theoretical results developed in this paper is verified by two numerical simulations.

Robust finite-time synchronization of non-identical fractional-order hyperchaotic systems and its application in secure communication

This paper proposes a novel adaptive sliding mode control &#x0028 SMC &#x0029 method for synchronization of non-identical fractional-order &#x0028 FO &#x0029 chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances, finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller &#x0028 ASMC &#x0029. Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization &#x0028 PSO &#x0029 is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.

Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros

ABSTRACTThis paper considers the finite-time synchronization of chaotic systems in the presence of model uncertainties and/or external disturbances. The synchronization happens between the two nonlinear master and slave systems. Control law is designed in such a way that the state variables of the slave system follow the state variables of the master system in the presence of uncertainties and external disturbances. In order to design a robust finite-time controller, first, a novel terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then a terminal sliding mode controller is designed which can conquer the uncertainties and guarantees the finite-time stability of the sliding motion equations. In this regard, a theorem is proposed and according to the Lyapunov approach it is proved that the synchronization happenes in finite-time. Additionally, in order to show the applicability of the proposed controller, it is applied on two practical systems, the Duffing–Holmes system and chaotic gyroscope system. Computer simulations verify the theoretical results and also display the effective performance of the proposed controller.

Robust finite-time synchronization of a class of chaotic systems via adaptive global sliding mode control

This paper proposes an adaptive robust finite-time control method based on a global sliding surface for the synchronization of a class of chaotic systems. New chattering-free control laws are designed to guarantee the removal of the reaching mode and realize the existence of the sliding mode around the designed surface right from the first moment. The proposed adaptive-tuning controllers eliminate the requirement of knowledge about disturbance bounds. Using the suggested control technique, superior master–slave synchronization is achieved, the chattering problem is fully solved, and the amplitudes of the control signals are noticeably decreased. Demonstrative simulation results for a Lü chaotic system are presented to indicate the efficiency and usefulness of the proposed scheme. In the end, using a state-feedback controller, we obtain a four-dimensional system with two interesting features. First, some hyperchaotic solutions are proposed, and then a continuous bifurcation diagram showing chaos for a wide range of bifurcation parameter is presented.

Finite-time synchronization control and parameter identification of uncertain permanent magnet synchronous motor

In this paper, the robust finite-time synchronization control and parameter identification problems for uncertain permanent magnet synchronous motor are discussed in detail. Based on finite-time control theory, by using adaptive control approach, a novel adaptive finite-time control scheme is proposed firstly. Then, a robust adaptive finite-time synchronization control method is developed depending on the terminal attractors with updating tuning parameters, which can not only guarantee the synchronization of permanent magnet synchronous motor with uncertain parameters in a shorter finite time, but also can guarantee these uncertain parameters to be identified effectively simultaneously. Finally, some simulation and comparison results are provided to demonstrate the effectiveness and usefulness of the developed results.

Robust finite-time global synchronization of chaotic systems with different orders

This article proves that the robust finite-time synchronization behavior can be achieved for the chaotic systems with different orders. Based on the Lyapunov stability theory and using the nonlinear feedback control, sufficient algebraic conditions are derived to compute the linear controller gains. These gains are then used to achieve the robust finite time increasing order and reduced order synchronization of the chaotic systems. This study also discusses the design of a controller that accomplishes the finite time synchronization of two chaotic systems of different dimensions under the effect of both unknown model uncertainties and external disturbances. Numerical simulation results are furnished to validate the theoretical findings.

Robust finite-time synchronization of coupled harmonic oscillations with external disturbance

This paper considers the problem of finite-time synchronization for multiple coupled harmonic oscillators with a leader–follower architecture. By using the techniques of finite-time control and saturation control, a class of bounded finite-time state feedback controllers are first proposed. Then to address the case in the presence of external disturbance and lack of velocity measurement, a finite-time convergent observer is constructed to estimate both the unknown velocity information and the disturbance in a finite time. Finally, a disturbance observer-based bounded finite-time output feedback controller is developed. Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leader׳s states.

Finite-time stochastic synchronization of genetic regulatory networks

This paper is concerned with the finite-time synchronization for a class of stochastic genetic regulatory networks (GRNs). The purpose of the addressed problem is to design a controller that can synchronize the concentration of the mRNA and the protein of GRNs in finite time with probability. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are first established for ensuring the finite-time stochastic stability of synchronization error in probability. Then, the gain parameters of the controller are obtained by solving a linear matrix inequality and the robust finite-time synchronization is guaranteed for GRNs with uncertain parameters. Compared with the previous references, a continuous finite-time controller is designed to achieve the synchronization objective and a constructive method that may accelerate the convergence is discussed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.

Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs

Centrifugal flywheel governors are known as chaotic non-autonomous mechanical devices used for automatic control of the speed of engines. The main characteristic of them is avoiding the damage caused by sudden change of the load torques. In this paper, the problem of robust finite-time synchronization of centrifugal flywheel governor systems is studied. The effects of unknown parameters, model uncertainties, external noises, and input nonlinearities are fully taken into account. We propose some adaptive laws to overcome the side effects of the unknown parameters of the system on the synchronization performance. Then, a robust adaptive switching controller is introduced to synchronize centrifugal flywheel governors with nonlinear control inputs in a given finite time. The finite-time fast convergence property of the proposed scheme is analytically proved and numerically illustrated.

Design of an adaptive finite-time controller for synchronization of two identical/different non-autonomous chaotic flywheel governor systems

The centrifugal flywheel governor (CFG) is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by sudden change of load torque. It has been shown that this system exhibits very rich and complex dynamics such as chaos. This paper investigates the problem of robust finite-time synchronization of non-autonomous chaotic CFGs. The effects of unknown parameters, model uncertainties and external disturbances are fully taken into account. First, it is assumed that the parameters of both master and slave CFGs have the same value and a suitable adaptive finite-time controller is designed. Second, two CFGs are synchronized with the parameters of different values via a robust adaptive finite-time control approach. Finally, some numerical simulations are used to demonstrate the effectiveness and robustness of the proposed finite-time controllers.