Disturbance rejection for multi-weighted complex dynamical networks with actuator saturation and deception attacks via hybrid-triggered mechanism

In this work, we address hybrid-driven-based robust synchronization problem for multi-weighted complex dynamical networks with actuator saturation and deception attacks. The hybrid-triggered mechanism, which combines a switch between the event-triggered scheme and the time-triggered scheme, is often used to reduce the data transmission and the alleviate network burden. Further, the equivalent-input-disturbance technique is applied to eliminate the unknown disturbance effect of the addressed system. Moreover, a memory controller is designed under actuator saturation to ensure that the resultant augmented system is asymptotically synchronized even in the presence of deception attacks. Finally, three numerical examples are given to show the validity of the obtained theoretical results.

Finite-time H∞ synchronization for complex dynamical networks with time-varying delays based on adaptive control

This paper investigates the problem of finite-time H_∞ synchronization (H_∞FTS) for complex dynamical networks (CDNs) with time-varying delays(TVDs) and unknown internal coupling matrices. External disturbances are also considered into this model. By applying the adaptive control theory, this paper presents the adaptive control method to solve the H_∞FTS of CDNs with external disturbances and TVDs. Some criteria are obtained by utilizing appropriate adaptive controllers and devising a special Lyapunov-Krasovskii function (LKF), which ensure the H_∞FTS of CDNs based on passivity theory. Finally, using some effective mathematical techniques, comparative numerical example and Chua's circuit system are used to explain the advantages and applicability of the results and approaches.

Non-fragile synchronization of complex dynamical networks with hybrid delays and stochastic disturbance via sampled-data control

This paper focuses on the global synchronization issue for a class of the complex dynamical networks (CDNs) with hybrid delays and stochastic disturbance. The hybrid delays consider two forms: discrete-time coupling delays and distributed coupling delays. The non-fragile sampled-data control protocol, which is allowed to norm-bounded uncertainty, is considered for the first time in this paper. Next, by applying a new augmented Lyapunov-Krasovskii functional (LKF), with the aid of the convex combination method and the stochastic analysis technique, a less conservative condition is derived to ensure that the considered CDNs can achieve the global synchronization with hybrid delays and stochastic disturbance under a non-fragile sampled-data control strategy. Finally, there exists three simulation examples to verify the effectiveness and advantages of the analytical results.

Disturbance and uncertainty rejection performance for fractional-order complex dynamical networks

This paper investigates the synchronization issue for a family of time-delayed fractional-order complex dynamical networks (FCDNs) with time delay, unknown bounded uncertainty and disturbance. A novel fractional uncertainty and disturbance estimator (FUDE) based feedback control strategy is proposed to not only synchronize the considered FCDNs but also guaranteeing the precise rejection of unmodelled system uncertainty and external disturbance. Especially, in FUDE-based approach, model uncertainties and external disturbance are integrated as a lumped disturbance and it does not require a completely known system model or a disturbance model. On the other hand, the design algorithm for the proposed control strategy is based on the state-space framework, rather than frequency-based design methodologies in the literature, which helps for predominant comprehension of the inner system behaviour. Also, by the temperance of Lyapunov stability theory and fractional calculus, a set of adequate conditions in the linear matrix inequality framework is obtained, which guarantees the robust synchronization of the closed-loop system. Furthermore, an iterative optimization algorithm is proposed to improve control robustness against the external disturbance and model uncertainties. Finally, two numerical illustrations including financial network model, where the influence of adjustment of macro-economic policies in the entire financial system are given to exhibit the rightness and important features of the acquired theoretical results.

New synchronization criteria for complex delayed dynamical networks with sampled-data feedback control

This paper investigates the synchronization problem for a class of complex delayed dynamical networks (CDDNs) by using sampled-data feedback control. First, an augmented Lyapunov-Krasovskii function (LKF) is constructed, which contains two new triple integral terms to reduce the conservativeness. Second, improved synchronization criteria are proposed by combining reciprocally convex technique with a novel class of integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. Third, the desired sampled-data controllers can be achieved by solving a set of linear matrix inequalities (LMIs). Finally, three numerical simulation examples are presented to demonstrate the effectiveness and advantages of the proposed results.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.

Synchronization criteria of discrete-time complex networks with time-varying delays and parameter uncertainties

This paper is pertained with the synchronization problem for an array of coupled discrete-time complex networks with the presence of both time-varying delays and parameter uncertainties. The time-varying delays are considered both in the network couplings and dynamical nodes. By constructing suitable Lyapunov-Krasovskii functional and utilizing convex reciprocal lemma, new synchronization criteria for the complex networks are established in terms of linear matrix inequalities. Delay-partitioning technique is employed to incur less conservative results. All the results presented here not only depend upon lower and upper bounds of the time-delay, but also the number of delay partitions. Numerical simulations are rendered to exemplify the effectiveness and applicability of the proposed results.