Fractional-order Complex Dynamical Networks Research Articles

Asymptotic and Pinning Synchronization of Fractional-Order Nonidentical Complex Dynamical Networks with Uncertain Parameters

This paper is concerned with the asymptotic and pinning synchronization of fractional-order nonidentical complex dynamical networks with uncertain parameters (FONCDNUP). First of all, some synchronization criteria of FONCDNUP are proposed by using the stability of fractional-order dynamical systems and inequality theory. Moreover, a novel controller is derived by using the Lyapunov direct method and the differential inclusion theory. Next, based on the Lyapunov stability theory and pinning control techniques, a new group of sufficient conditions to assure the synchronization for FONCDNUP are obtained by adding controllers to the sub-nodes of networks. At last, two numerical simulations are utilized to illustrate the validity and rationality of the acquired results.

Saturated delayed impulsive effects for fractional order nonlinear system with piecewise Caputo derivative and its application

Fractional order nonlinear systems with saturated delayed impulses and short-term memory is investigated in this paper. Models in this paper are described by piecewise Caputo derivative. First, sufficient conditions for local exponential stability are derived based on the fractional order Lyapunov function method and saturated control theory. Then, the optimization model to estimate the domain of attraction is built, which is constrained by some LMIs. Third, the application of synchronization for fractional order complex dynamical networks via distributed saturated delayed impulsive control is studied. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.

Robust synchronization of multi-weighted fractional order complex dynamical networks under nonlinear coupling via non-fragile control with leakage and constant delays

In this article, we examine the impact of leakage delays on robust synchronization for fractional order multi-weighted complex dynamical networks(MFCDN) under non-linear coupling via non-fragile control. By employing the fractional order comparison principle, suitable Lyapunov method, and some fractional order inequality techniques, we ensured the robust asymptotical synchronization for MFCDN. In addition to common findings, we have done some specific research in order to get reliable synchronization for multi-weighted complex dynamical network(MCDN) without leakage delay. Additionally, our findings gained are applicable to single weighted FCDN and integer order complex dynamical networks, regardless of whether they have a single weight or many weights. Our suggested approach is shown to be more effective and practical in this article by providing a numerical simulation.

Passivity and Finite-Time Passivity for Multi-Weighted Fractional-Order Complex Networks With Fixed and Adaptive Couplings.

This article presents several new α -passivity and α -finite-time passivity ( α -FTP) concepts for the fractional-order systems with different input and output dimensions, which are distinct from the concepts for integer-order systems and extend the existing passivity and FTP definitions to some extent. On one hand, we not only develop some sufficient conditions for ensuring the α -passivity of the multi-weighted fractional-order complex dynamical networks (MWFOCDNs) with fixed and adaptive couplings, but also discuss the synchronization for the MWFOCDNs based on the α -output-strict passivity ( α -OSP). On the other hand, the α -FTP for the MWFOCDNs with fixed and adaptive couplings are also studied on the basis of the designed state feedback controller, and the relationship between finite-time synchronization (FTS) and α -FTP for the MWFOCDNs is also illustrated. Finally, two numerical examples with simulation results are used to demonstrate the validity of the obtained criteria.

Asymptotic Synchronization of Fractional-Order Complex Dynamical Networks with Different Structures and Parameter Uncertainties

This paper deals with the asymptotic synchronization of fractional-order complex dynamical networks with different structures and parameter uncertainties (FCDNDP). Firstly, the FCDNDP model is proposed by the Riemann–Liouville (R-L) fractional derivative. According to the property of fractional calculus and the Lyapunov direct method, an original controller is proposed to achieve the asymptotic synchronization of FCDNDP. Our controller is more adaptable and effective than those in other literature. Secondly, a sufficient condition is given for the asymptotic synchronization of FCDNDP based on the asymptotic stability theorem and the matrix inequality technique. Finally, the numerical simulations verify the effectiveness of the proposed method.

Disturbance rejections and synchronization of fractional-order fuzzy complex networks

This paper deals with the problem of disturbance rejection and synchronization of fractional-order complex dynamical networks subject to nonlinear coupling strength and discontinuous nonlinear functions. Notably, the nonlinear coupling strength is linearised by using a well-known Takagi-Sugeno fuzzy approach. The considered system is transformed into a nominal form by employing the uncertainty and disturbance estimator-based control approach, which simplifies the control objective and improves the system performance. Second, the uncertainty and disturbance estimator is incorporated into the traditional feedback control scheme to reject the unknown disturbance and uncertainty. Then, the required synchronization conditions for both the discontinuous and continuous fractional-order systems are obtained by using Lyapunov stability and fractional calculus theories. Last, numerical examples are provided to illustrate the efficiency of the proposed control strategy, wherein it is shown that the system yields better satisfactory tracking performance and high robustness against possible disturbance and uncertainties and finite set of jump discontinuous nonlinear functions. Moreover, the selection of appropriate filter design is discussed for various kinds of disturbance signals.

Finite-Time Projective Synchronization and Parameter Identification of Fractional-Order Complex Networks with Unknown External Disturbances

This paper is devoted to exploring the finite-time projective synchronization (FTPS) of fractional-order complex dynamical networks (FOCDNs) with unknown parameters and external disturbances. Based on the stability theory of fractional-order differential systems, synchronization criteria between drive-response networks were obtained and both the uncertain parameters and external disturbances were identified or conquered simultaneously. Moreover, the upper limit of the settling-time function was obtained. Finally, a numerical example was given to verify the effectiveness of the results.

Impulsive Exponential Synchronization of Fractional-Order Complex Dynamical Networks with Derivative Couplings via Feedback Control Based on Discrete Time State Observations

Impulsive Exponential Synchronization of Fractional-Order Complex Dynamical Networks with Derivative Couplings via Feedback Control Based on Discrete Time State Observations

Comparison principle and synchronization analysis of fractional-order complex networks with parameter uncertainties and multiple time delays

<abstract><p>This paper investigates the global synchronization problems of fractional-order complex dynamical networks with uncertain inner coupling and multiple time delays. In particular, both internal time delays and coupling time delays are introduced into our model. To overcome the difficulties caused by various delays and uncertainties, a generalized delayed comparison principle with fractional-order and impulsive effects is established by using the Laplace transform. Based on the Lyapunov stability theory and mixed impulsive control technologies, some new synchronization criteria for concerned complex dynamical networks are derived. In addition, the synchronization criteria are related to the impulsive interval, network topology structure, fractional-order, and control gains. The theoretical results obtained in this paper can enhance the value of previous related works. Finally, numerical simulations are presented to show the correctness of our main results.</p></abstract>

Identifying topology and system parameters of fractional-order complex dynamical networks

This article aims to identify the topology and system parameter of fractional-order complex dynamical networks. The unknown topology and system parameter of the drive network are successfully identified under several controllers and update strategies. Moreover, we propose a lemma as the necessary condition to ensure successful identification. Two numerical simulations conclude that the high heterogeneity between the nodes of the drive network facilitates identification.

Non-periodically intermittent exponential synchronization of fractional-order multi-links complex dynamical networks

In this paper, the exponential synchronization of fractional-order multi-links complex dynamical networks (CDNs) is studied based on non-periodically intermittent control. By means of the Lyapunov method and graph-theoretic approach, a Lyapunov-type theorem is provided based on the existence of vertex-Lyapunov functions. Then by giving the specific vertex-Lyapunov functions, a coefficients-type theorem is presented where the conditions of it are based on the coefficients of system. Moreover, to show the practicality of theoretical results, we give two applications to fractional-order chaotic CDNs with multiple links and fractional-order Hindmarsh–Rose neuron systems with multiple links, respectively. Meanwhile, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results.

Intermittent control for finite-time synchronization of fractional-order complex networks

This paper is concerned with the finite-time synchronization problem for fractional-order complex dynamical networks (FCDNs) with intermittent control. Using the definition of Caputo’s fractional derivative and the properties of Beta function, the Caputo fractional-order derivative of the power function is evaluated. A general fractional-order intermittent differential inequality is obtained with fewer additional constraints. Then, the criteria are established for the finite-time convergence of FCDNs under intermittent feedback control, intermittent adaptive control and intermittent pinning control indicate that the setting time is related to order of FCDNs and initial conditions. Finally, these theoretical results are illustrated by numerical examples.

Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control

Adaptive modified projective function synchronization of non-linear distributive fractional order complex dynamical networks (DFCDN) is addressed in this paper. Firstly, we have created a model for DFCDN with model uncertainty, external disturbances and uncertain parameters. Based on the Laplace and inverse Laplace transform property of distributive order fractional differential equations and Lyapunov stability theory, we realize the projective synchronization between the DFCDN system, according to the given scaling function by using the novel adaptive controller that we have constructed. Finally two numerical examples and simulations are given to show our proposed work is more realistic and more effective than the existing ones in the literature.

Observer-based synchronization of fractional-order Markovian jump multi-weighted complex dynamical networks subject to actuator faults

This paper is concerned with an observer-based robust H∞ synchronization problem for a class of fractional-order multi-weighted complex dynamical networks subject to Markovian jump parameters, actuator faults and time-varying coupling delay by using fault-tolerant control scheme. The considered actuator fault model is a general one, which consisting of both linear and nonlinear fault terms. Further, by employing a continuous frequency distributed equivalent model and using indirect Lyapunov approach, a new set of sufficient conditions is derived to ensure the asymptotic synchronization of the addressed system in the mean square sense with a prescribed H∞ performance index. In particular, by constructing monochromatic Lyapunov functional and utilizing extended Wirtinger-based integral inequality the required sufficient conditions are developed in terms of linear matrix inequalities. Finally, two numerical examples including financial model are provided to illustrate the effectiveness of the obtained results.

Topology identification of fractional-order complex dynamical networks based on auxiliary-system approach.

Many practical systems can be well described by various fractional-order equations. This paper focuses on identifying the topology of the response layer of a drive-response fractional-order complex dynamical network using the auxiliary-system approach. Specifically, the response layer and the auxiliary layer receive the same input signals from the drive layer. By a designed adaptive control law, the unknown topology of the response layer is successfully identified. Moreover, the proposed method is effective even if the drive layer is made up of isolated nodes. The correctness of the theoretical results is demonstrated by numerical simulations.

Pinning exponential cluster synchronization for fractional-order complex dynamical networks with switching topology and mode-dependent impulses

In this paper, we focus on the global exponential cluster synchronization of switched fractional-order complex dynamical networks (FCDNs) with switching topology and impulses, where the impulse effects are independent or dependent of switched modal. Compared with the literature, impulsive effects can occur not at the mode switched moment, but also at the instants without me AII) with the average dwell time (ADT) and the mode-dependent average impulsive interval (MDAII) with the mode-dependent average dwell time, by adopting multiple Lyapunov functional approach, the inequality analysis technique and pinning control strategy, the global exponential cluster synchronization conditions are achieved. Finally, the validity of theoretical results is verified by two simulation examples.

Exponential quasi-synchronization of conformable fractional-order complex dynamical networks

Abstract This article concerns the global exponential quasi-synchronization issue of conformable fractional-order complex dynamical networks (FCDNs) by periodically intermittent pinning control. We first establish two conformable fractional-order differential inequality, which are useful to deal with the global exponential quasi-synchronization of conformable FCDNs, and then by the obtained inequalities, the Lyapunov approach as well as the periodically intermittent pinning controller, related sufficient conditions are obtained to ensure the global exponential quasi-synchronization of the addressed networks. Finally, numerical simulations are provided to show the effectiveness of the theoretical results.

Robust synchronization in finite time for fractional-order hybrid coupling discontinuous complex dynamic networks with nonlinear growth

In this paper, the global robust synchronization and synchronization in finite time are considered for fractional-order hybrid coupling complex dynamical networks (CDNs), where the growth of dynamic nodes is discontinuous, and subjected to a quadratic polynomial. Firstly, a convergence principle in finite time is developed for fractional-order nonlinear systems with discontinuous right-hand side. Secondly, a suitable discontinuous controller without the terms of time delays is designed, and the global robust synchronization condition is addressed in the terms of linear matrix inequalities (LMIs) by applying Lyapunov functional approach, inequality analysis technique, and Clarke’s non-smooth analysis method. In addition, the global robust synchronization goal in finite time is achieved by utilizing the developed convergence principle. Moreover, the upper bound of the settling time for the global robust synchronization in finite time is explicitly evaluated. Finally, the feasibility of the proposed design scheme and the validity of theoretical results are verified by two numerical simulation examples.

Observer-based robust synchronization of fractional-order multi-weighted complex dynamical networks

In this paper, the problem of robust synchronization of fractional-order multi-weighted complex dynamical networks in the presence of time-varying coupling delay and disturbances is studied via fractional-order equivalent-input-disturbance (FOEID) estimator-based non-fragile feedback control scheme. Precisely, FOEID-based disturbance estimator is incorporated in the feedback control input to compensate the disturbance effect in the resulting closed-loop system, which removes the disturbance effect without any prior knowledge of it. By utilizing FOEID method and synchronization error dynamics, the synchronization problem of fractional-order complex dynamical network is transformed into the stability problem of the augmented form of the closed-loop error system. Based on the Lyapunov stability theory, fractional calculus theory and some advanced integral inequalities, a novel set of sufficient conditions is established to ensure the robust asymptotic stability of the augmented error system subject to time-varying delay and disturbances. Finally, two numerical examples including a comparison study are given to illustrate the obtained theoretical results and the control design.

Finite-time synchronization for different dimensional fractional-order complex dynamical networks

This article is involved with the finite-time synchronization problem between two different dimensional fractional-order complex dynamical networks (FOCDNs). Firstly, the definition of finite-time synchronization for different dimensional FOCDNs are introduced. Under the framework of finite-time control theory and fractional-order Lyapunov functional method, the controller is designed such that the FOCDNs are synchronized in a finite time. Secondly, some unknown parameters are adopted in the FOCDNs, novel adaptive updated control law and dynamical parameter estimation are proposed to guarantee that the finite-time synchronization can be obtained to achieve the desired conclusions. Furthermore, the setting times for synchronization of FOCDNs are explicitly evaluated. Finally, a numerical example is presented to demonstrate the effectiveness of proposed control algorithms.