Drive-response Dynamical Networks Research Articles

Parameter identification based on lag synchronization via hybrid feedback control in uncertain drive-response dynamical networks

In this paper, we use a hybrid feedback control method to study lag synchronization in uncertain drive-response dynamical networks with a feature that the unknown system parameter exists in the node dynamics. We then design two hybrid feedback control methods to achieve the lag synchronization including the linear and adaptive feedback control. With the designed controllers and update laws for the system parameter in the node dynamics, we obtain two theorems on the lag synchronization based on the LaSalle invariance principle. When the lag synchronization is achieved, we identify the unknown system parameter. Finally, we provide two numerical examples to verify the efficiency of the proposed control schemes.

Robust projective lag synchronization in drive-response dynamical networks via adaptive control

This paper investigates the problem of projective lag synchronization behavior in drive-response dynamical networks (DRDNs) with identical and non-identical nodes. An adaptive control method is designed to achieve projective lag synchronization with fully unknown parameters and unknown bounded disturbances. These parameters were estimated by adaptive laws obtained by Lyapunov stability theory. Furthermore, sufficient conditions for synchronization are derived analytically using the Lyapunov stability theory and adaptive control. In addition, the unknown bounded disturbances are also overcome by the proposed control. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Simulation results show the effectiveness of the proposed method.

Adaptive projective lag synchronization of uncertain complex dynamical networks with delay coupling

This paper investigates the problem of projective lag synchronization behavior with delayed coupling in drive-response dynamical networks model with identical and non-identical nodes. An adaptive control method is designed to achieve the projective lag synchronization with constant time delay and with time-varying coupling delay. In addition the model harbors fully unknown parameters and disturbances. By using Lyapunov stability theory and adaptive laws, the unknown parameters are estimated. In addition, the unknown bounded mismatch and disturbance terms are also overcome by the proposed control. Finally, the simulation results reveal that the states of the dynamical network with delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Additionally, the results prove the validity of the proposed method.

Projective lag synchronization in drive-response dynamical networks with delay coupling via hybrid feedback control

This paper investigates the problem of projective lag synchronization behavior with delayed coupling in drive-response dynamical network model consisting of identical and nonidentical nodes. Based on Lyapunov stability theory, a hybrid feedback control method is designed to achieve the projective lag synchronization with constant time delay and with time-varying coupling delay. In addition, the control will deal with and without mismatched terms. Finally, analytical results show that the states of the dynamical network with delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulation results demonstrate the validity of the proposed method.

Outer synchronization of drive-response dynamical networks via adaptive impulsive pinning control

In this paper, outer synchronization between drive and response networks via adaptive impulsive pinning control is investigated. In the pinning control scheme, the controlled nodes are changed adaptively according to the synchronization errors at different impulsive instants. Based on the Lyapunov function method and mathematical analysis, a synchronization criterion is precisely derived. Under this criterion, the impulsive intervals for achieving outer synchronization of two given networks are estimated. Further, an adaptive strategy is designed for a node-to-node pinning impulsive controller, with a corresponding synchronization condition derived. In the 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 developed and evaluated. The theoretical results are illustrated to be effective by several numerical examples.

The Projective Synchronization of Drive-Reponse Complex Dynamical Networks

This paper investigates the projective synchronization of drive-response complex dynamical networks. Based on the stability theory for fractional-order differential equations, controllers are designed torealize the projective synchronization for complex dynamical networks. Morover, some simple synchronization conditions are proposed. Numerical simulations are presented to show the effectiveness of the proposed method.

Projective lag synchronization in drive-response dynamical networks

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

Adaptive Impulsive Outer Synchronization Between Drive-Response Dynamical Networks

In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the Lyapunov function method and mathematical analysis technique, a synchronization criterion with respect to the impulsive gains and intervals is analytically derived. From the criterion, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some constants are fixed, and vice versa. Finally, two numerical examples are provided to verify the effectiveness of the derived result.

Weak Projective Synchronization in Drive-Response Dynamical Networks with Time-Varying Delay and Parameter Mismatch

This paper investigates the problem of projective synchronization in drive-response dynamical networks (DRDNs) with time-varying delay and parameter mismatch via impulsive control. Owing to projective factor and parameter mismatch, complete projective synchronization cannot be achieved. Therefore, a weak projective synchronization scheme is proposed to ensure that the DRDNs are in a state of synchronization with an error level. Based on the stability analysis of the impulsive functional differential equations, a general method of the weak projective synchronization with the error level is derived in DRDNs. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.

Projective Synchronization Analysis of Drive-Response Coupled Dynamical Network with Multiple Time-Varying Delays via Impulsive Control

The problem of projective synchronization of drive-response coupled dynamical network with delayed system nodes and multiple coupling time-varying delays is investigated. Some sufficient conditions are derived to ensure projective synchronization of drive-response coupled network under the impulsive controller by utilizing the stability analysis of the impulsive functional differential equation and comparison theory. Numerical simulations on coupled time delay Lorenz chaotic systems are exploited finally to illustrate the effectiveness of the obtained results.

Synchronization in Drive-Response Dynamical Networks Based on Nonlinear Control

In this paper, synchronization in drive-response dynamical networks is investigated. By using the Gerschgorins disk theorem and the stability theory, a nonlinear controller is designed to make the drive-response dynamical networks synchronized. Some sufficient conditions for achieving the synchronization of the drive-response dynamical networks are derived. The structure of the network can be random, regular, small-world, or scale-free. A numerical example is given to demonstrate the validity of the proposed method, in which the famous Lorenz system is chosen as the nodes of the network. Simulation results have verified the correctness and effectiveness of the proposed scheme. Moreover, it is worth noting that the time used for achieving synchronization of the drive-response dynamical networks sensitively depends on the coupling strength .

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization (FPS) in drive—response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.

Adaptive pinning control for the projective synchronization of drive-response dynamical networks

This paper studies the projective synchronization of a drive-response dynamical network of partially linear systems. The coupling-configuration matrix of the network is not necessarily symmetric. Two adaptive pinning control strategies are derived based on the Barbalat’s Lemma. In the first control strategy, the pinning control gain is adaptively updated to realize the projective synchronization. In the second control strategy, both the pinning control gain and the coupling strength between nodes are adaptively updated. Numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network.

Analyzing projective synchronization on different scaling factors in a drive-response coupling dynamical network with time-varying delays

In this paper, projective synchronization of drive-response coupled dynamical network with delayed system nodes and coupling time-varying delay is investigated via impulsive control, where the scaling factors are different from each other. Different controllers are designed to achieve the projective synchronization: only impulsive control is used when the scaling factors need extra limitation, while an extra controller, that is, a simple linear feedback controller, is added when the scaling factors don’t need extra limitation. Based on the stability analysis of the impulsive functional differential equation, the sufficient conditions for achieving projective synchronization of such coupled network are established, and an estimate of the upper bound of impulsive intervals ensuring global exponential synchronization of drive-response coupled dynamical network is also given. Numerical examples on the time-delay Lorenz chaotic systems are presented finally to illustrate the effectiveness and advantage of the proposed synchronization criteria.

Adaptive Generalized Projective Synchronization of Takagi-Sugeno Fuzzy Drive-response Dynamical Networks with Time Delay

Time-delay Takagi-Sugeno fuzzy drive-response dynamical networks (TD-TSFDRDNs) are defined by extending the drive-response dynamical networks. Based on the LaSalle invariant principle, a simple and systematic adaptive control scheme is proposed to synchronize the TD-TSFDRDNs with a desired scalar factor. A sufficient condition for the generalized projective synchronization in TD-TSFDRDNs is derived. Moreover, numerical simulations are provided to verify the correctness and effectiveness of the scheme.

Adaptive open-plus-closed-loop method of projective synchronization in drive-response dynamical networks

This paper investigates the problem of projective synchronization (PS) in drive-response dynamical networks (DRDNs) with mismatched terms. Based on the adaptive open-plus-closed-loop (AOPCL) method, a general method of PS is derived in DRDNs, which is robust to limited accuracy of data and effects of noise. Moreover, the feedback gains of the closed loop control part can be automatically adapted to suitable constants. Corresponding numerical simulations on Lorenz system are performed to verify and illustrate the analytical results.

ADAPTIVE OPEN-PLUS-CLOSED-LOOP CONTROL METHOD OF MODIFIED FUNCTION PROJECTIVE SYNCHRONIZATION IN COMPLEX NETWORKS

This paper investigates the modified function projective synchronization (MFPS) in drive-response dynamical networks (DRDNs) with different nodes, which means that systems in nodes are strictly different. An adaptive open-plus-closed-loop (AOPCL) control method is proposed, which is a practically realizable method and can overcome the model mismatched to achieve synchronization. It is well known that each of the close-loop and open-loop control method possesses some advantages and disadvantages. By combining their advantages, the open-plus-closed-loop (OPCL) control method was proposed by Jackson and Grosu. For arbitrary nonlinear dynamic systems, dx/dt = F(x,t), Jackson and Grosu proved that there exists solutions, x(t), in the neighborhood of any arbitrary goal dynamics g(t) that are entrained to g(t), through the use of an additive controlling action, K(g,x,t) = H(dg/dt,g) + C(g,t)(g(t) - x), which is the sum of the open-loop action, H(dg/dt,g), and a suitable linear closed-loop (feedback) action C(g,t). This method is a practically realizable method and robust to limited accuracy of data and effects of noise. The AOPCL control method preserve the merits of OPCL control method and its closed loop control part can be automatically adapted to suitable constants. Considering time-delays are always unavoidably in the practical situations, MFPS in DRDNs with time-varying coupling delayed is further investigated by the proposed method. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

Function projective synchronization in drive–response dynamical networks with non-identical nodes

This paper investigates the problem of function projective synchronization (FPS) in drive–response dynamical networks (DRDNs) with non-identical nodes. Based on the adaptive open-plus-closed-loop (AOPCL) method, a general method of function projective synchronization is derived, which is robust to limited accuracy of data and effects of noise. Corresponding numerical simulations on the Lorenz system are performed to verify and illustrate the analytical results.

Projective synchronisation with non-delayed and delayed coupling in complex networks consisting of identical nodes and different nodes

This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes. Based on Lyapunov stability theory, several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks; simultaneously the topological structure of the drive dynamical complex networks can be exactly identified. Moreover, numerical examples are presented to verify the feasibility and effectiveness of the theorems.

Function projective synchronization in drive–response dynamical network

In this Letter, the function projective synchronization in the drive–response dynamical network is investigated, where the response dynamical network is affected not only by the drive system, but also coupled via a linearly feedback scheme. Based on Lyapunov stability theory, it is shown that the function projective synchronization with desired scaling function can be realized in the drive–response dynamical network by a simple control law. Moreover it is no need for the scaling function to be differentiable, bounded and nonzero all the time. The numerical simulations are provided to verify the theoretical result.