Conservative Synchronization Criteria Research Articles

Submission to Special Issue to Explainable Representation Learning-Based Intelligent Inspection and Maintenance of Complex Systems: Synchronization of Inertial Neural Networks With Unbounded Delays via Sampled-Data Control.

This article addresses the synchronization issue for inertial neural networks (INNs) with heterogeneous time-varying delays and unbounded distributed delays, in which the state quantization is considered. First, by fully considering the delay and sampling time point information, a modified looped-functional is proposed for the synchronization error system. Compared with the existing Lyapunov-Krasovskii functional (LKF), the proposed functional contains the sawtooth structure term V8(t) and the time-varying terms ex(t-βħ (t)) and ey(t-βħ (t)) . Then, the obtained constraints may be further relaxed. Based on the functional and integral inequality, less conservative synchronization criteria are derived as the basis of controller design. In addition, the required quantized sampled-data controller is proposed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness and superiority of the proposed scheme in this article.

Mixed-Delay-Based Augmented Functional for Sampled-Data Synchronization of Delayed Neural Networks With Communication Delay.

The synchronization control for delayed neural networks (DNNs) via a sampled-data controller considering communication delay is studied by input delay approach. Although few scholars have put forward the coexistence of transmission delay and communication delay in this problem, no report has clarified the interaction between transmission delay and communication delay. Also, the time-squared terms are underutilized. Thus, a novel augmented Lyapunov functional, which consists of a mixed-delay-based augmented part and a time-squared two-sided looped part, is proposed to fill this gap. In the mixed-delay-based augmented part, not only the information of transmission delay and communication delay themselves, but also the interaction between those two delays is considered. Time-dependent quadratic terms as well as the sampling integral states are introduced in the two-sided looped part, so that more characteristic information of the sampling pattern is encompassed and the relationship of the states at the sampling instant is enhanced. Then, this novel augmented functional is applied to the synchronization control of DNNs. A less conservative synchronization criterion is obtained in the form of linear matrix inequalities. A numerical example illustrates the validity and superiority of the presented synchronization criterion.

On Master-Slave Synchronization of Chaotic Lur’e Systems Using Sampled-Data Control

This brief aims to achieve a less conservative master-slave synchronization criterion for chaotic Lur’e systems using sampled-data control. To this end, a novel piecewise differentiable Lyapunov-Krasovskii functional (LKF) is constructed to fully capture the characteristics about real sampling pattern and nonlinearities of the system. By using the new LKF, a less conservative synchronization criterion is presented to guarantee global exponential stability about synchronization error system. Chua’s circuit system is adopted to verify effectiveness and advantage of obtained approach.

Synchronization of discrete-time fractional fuzzy neural networks with delays via quantized control

In this paper, synchronization issue of discrete-time fractional fuzzy neural networks (DFFNNs) with delays is solved via quantized control, and is applied in image encryption. Firstly, a novel fractional-order h-difference inequality which makes Lyapunov method more flexible and practical is strictly proved based on the properties of convex functions and theory of discrete fractional calculus. Secondly, by using compression mapping theorem and mathematical induction, we obtain two sufficient conditions to ensure the existence and uniqueness of solutions for DFFNNs. Whereafter, we design a suitable quantized controller, which not only saves channel resources but also reduces control costs. By utilizing our inequality and some analytical techniques, several conservative synchronization criteria for DFFNNs are acquired. Finally, two examples are arranged to illustrate the validity and practicability of our results.

Intermittent sampled-data control for exponential synchronization of chaotic delayed neural networks via an interval-dependent functional

This paper focuses on the exponential synchronization of chaotic delayed neural networks (CDNNs) via the intermittent sampled-data control (ISC). To save the control cost and limited bandwidth, an ISC strategy which integrates the merits of the intermittent control (IC) scheme and the sampled-data control (SC) scheme is proposed. With the proposed ISC scheme, an interval-dependent Lyapunov functional (IDLF) is established for the synchronization control systems. The main characteristic of this functional is that it takes full advantage of the available state information of both working intervals and sleeping intervals. Due to the continuity of the proposed functional, some restrictive conditions on Lyapunov matrices are removed. In addition, some less conservative synchronization criteria are established by means of a combination of the Lyapunov stability theory, the reciprocally convex inequality and the Wirtinger inequality. Meanwhile, an algorithm for the ISC gain is effectively designed to realize the synchronization of master and slave CDNNs. Furthermore, a qualitative relationship between the duty ratio (DR) and the system decaying rate is analyzed. In the end, two examples are given to reveal that the proposed results are feasible and reasonable.

An Improved Result on Sampled-Data Synchronization of Markov Jump Delayed Neural Networks

This article deals with the issue of dissipative synchronization for Markov jump neural networks subject to time-varying interval delays by using the sampled-data control method. First, a new two-sided looped-functional is introduced to improve the informativeness of the formed Lyapunov-Krasovskii functional, which takes into an account the information of the entire sampling period. Compared with some traditional methods, the information between x(t) and x(t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</sub> ) is also emphasized. On this basis, an improved inequality technique is considered valid to acquire the less conservative synchronization criterion. In the end, two numerical examples are displayed, and a comparative example powerfully demonstrates the availability and the superiority of the developed technique.

Sampled-Data Synchronization Control for Chaotic Neural Networks With Mixed Delays: A Discontinuous Lyapunov Functional Approach

The sampled-data synchronization problem of chaotic neural networks with mixed time delays is investigated in this paper. A novel augmented discontinuous Lyapunov-Krasovskii functional (ADLKF) is constructed, which can make full capture the more information of delay variation and the characteristics about the actual sampling information. Based on the ADLKF and modified free-matrix-based integral inequality, novel less conservative synchronization criteria are developed to guarantee that the slave system is synchronous with the master system. Furthermore, the derived results are given in terms of simplified linear matrix inequalities (LMIs), which can be straightforwardly solved by Matlab. Finally, two numerical examples are proposed to demonstrate the effectiveness and the benefits of the presented synchronization scheme.

Drive-response synchronization of uncertain Markov jump generalized neural networks with interval time varying delays via decentralized event-triggered communication scheme

This paper investigates the synchronization problem of uncertain Markov jump generalized neural networks with interval time varying delays using decentralized event-triggered approach. We present a decentralized event-triggered scheme is utilized to decide if the sensor estimations ought to be sent out or not. Every sensor can choose the transmitted sensor estimations locally as indicated by the related event-triggered condition. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) both continuous and discontinuous LKF, handled by the Jensen’s inequality, peng-park’s inequality (PPI) and a new Wirtinger-based integral inequality (WII) technique respectively. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The Lyapunov method is employed to derive a sufficient condition such that the error system is stochastically stable. Moreover, the desired controller gains and event-triggered parameters are derived provided that the sufficient condition is satisfied. Finally, numerical examples are included to show that the results obtained from the proposed method provide less conservative results, which support the superiority of our criteria.

Finite-Time Dissipative Synchronization for Markovian Jump Generalized Inertial Neural Networks With Reaction–Diffusion Terms

A novel generalized neural network (NN), which includes Markovian jump parameters, inertial items, and reaction-diffusion terms, is proposed, and the issue of finite-time dissipative synchronization for this kind of NNs is discussed in this article. First, an appropriate variable substitution is employed so that the original second-order differential system is transformed into a first-order one. Second, a novel time-varying memory-based controller is designed to ensure the dissipative synchronization of the drive and response systems over a finite-time interval. Then, a new Lyapunov-Krasovskii function is processed by reciprocally convex combination and free-weighting matrix methods, therefore, a less conservative synchronization criterion is derived. Finally, by providing three examples, the feasibility, superiority, and practicality of the obtained results are illustrated.

Finite-time nonfragile time-varying proportional retarded synchronization for Markovian Inertial Memristive NNs with reaction–diffusion items

The issue of synchronization for a class of inertial memristive neural networks over a finite-time interval is investigated in this paper. Specifically, reaction–diffusion items and Markovian jump parameters are both considered in the system model, meanwhile, a novel nonfragile time-varying proportional retarded control strategy is proposed. First, a befitting variable substitution is invoked to transform the original second-order differential system into a first-order one so that the corresponding synchronization error system that is represented by a first-order differential form is established. Second, by utilizing the integral inequality technique, reciprocally convex combination approach and free-weighting matrix method, a less conservative synchronization criterion in terms of linear matrix inequalities is obtained. Finally, three simulations are exploited to illustrate the feasibility, practicability and superiority of the designed controller so that the acquired theoretical results are supported.

Pinning Event-Triggered Sampling Control for Synchronization of T–S Fuzzy Complex Networks With Partial and Discrete-Time Couplings

This paper focuses on the synchronization problem of Takagi-Sugeno (T-S) fuzzy complex networks with partial and discrete-time couplings via event-triggered sampling control. Different from traditional control methods, a more general and practical event-triggered communication scheme with nonuniform sampling is newly designed for T-S fuzzy complex networks. Then, a Lyapunov-Krasovskii functional (LKF) with a novel input-delay-product-type (IDPT) term is presented. The IDPT term can fully capture the information of the nonlinear functions and the actual sampling pattern. Based on the new IDPT LKF, less conservative synchronization criteria are derived. Meanwhile, by solving a set of linear matrix inequalities, the desired pinning control gains are precisely obtained. Simulation examples are provided to illustrate the effectiveness and superiorities of the proposed results.

A new method for quantized sampled-data synchronization of delayed chaotic Lur’e systems

• The extended Wirtinger-inequality-based Lyapunov approach is newly proposed. • A zero equality is formulated, which can capture the information of system at the dynamic partitioning point. • A quantized sampled-data controller is designed. • Compared with some existing results, less conservative synchronization criteria are established for chaotic Lur’e systems. We design a quantized sampled-data controller for synchronization of delayed chaotic Lur’e systems. A new approach, extended Wirtinger-inequality-based Lyapunov–Krasovskii functional, is firstly proposed. This approach grasps more sampling information by introducing more free matrices in comparison with some existing methods. Using the system information at the dynamic partitioning point, a zero equality is formulated to fully utilize the inner sampling information. Based on the new approach and zero equality, some novel synchronization criteria are established. In the meantime, the desired quantized sampled-data control gain is obtained with larger sampling period than those in the existing works. Finally, two numerical examples illustrate the merits of the method.

Nonfragile Sampled-Data Synchronization for Delayed Complex Dynamical Networks With Randomly Occurring Controller Gain Fluctuations

In this paper, the problem of nonfragile sampled-data synchronization of delayed complex dynamical networks with randomly occurring controller gain fluctuations (ROCGFs) is studied. First, more applicable nonfragile memory sampled-data controllers are designed, which involve the signal transmission delay and ROCGFs. The controller gain fluctuations appear in a random way, which obey certain Bernoulli distributed white noise sequences. Second, a modified piecewise Lyapunov-Krasovskii functional (LKF), which involves cubic sawtooth structure term, is constructed for the first time. Third, based on the LKF, less conservative synchronization criteria are established. In comparison with the existing results, the constraint condition of the positive definition of the LKF is less restrictive, since it does not need to be positive definite for all time, but is only required to be positive definite at sampling times. Finally, the effectiveness and advantages of the obtained results are illustrated by two numerical examples.

Pinning outer synchronization of partially coupled dynamical networks with complex inner coupling matrices

This paper investigates outer synchronization of partially coupled dynamical networks with complex inner coupling matrices via pinning impulsive controller. At first, we establish more realistic drive–response partially coupled networks, where the inner coupling matrices between coupled nodes can be non-full rank and also asymmetric. Then, a weighted-norm-based method is given to select the nodes that should be pinning controlled, and our synchronization criteria derived by this method can be proved to be less conservative. By using the regrouping method and our new average impulsive interval method, some efficient and less conservative synchronization criteria are derived. Our results show that the outer synchronization can be achieved by impulsively controlling a crucial fraction of nodes in the response network. Finally, numerical examples are exploited to illustrate the effectiveness of our theoretical results.

Quantized Sampled-Data Control for Synchronization of Inertial Neural Networks With Heterogeneous Time-Varying Delays.

This paper is concerned with the problem of synchronization for inertial neural networks (INNs) with heterogeneous time-varying delays (HTVDs) through quantized sampled-data control. The control scheme, which takes the communication limitations of quantization and variable sampling into account, is first employed for tackling the synchronization of INNs. A novel Lyapunov-Krasovskii functional (LKF) is constructed for synchronizing an error system. Compared with existing LKFs by the largest upper bound of all HTVDs, the proposed LKF is superior, since it can make full use of the information on the lower and upper bounds of each HTVD. Based on the LKF and a new integral inequality technique, less conservative synchronization criteria are derived. The desired quantized sampled-data controller is designed by solving a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and conservatism reduction of the proposed results.

Pinning stochastic sampled-data control for exponential synchronization of directed complex dynamical networks with sampled-data communications

This paper is concerned with the exponential synchronization of directed complex dynamical networks (CDNs) with sampled-data communications (SDCs) via pinning stochastic sampled-data control. Different from traditional directed CDNs with determined sampling intervals, multiple stochastic varying sampling intervals with given probabilities are considered in this paper. Compared with some existing control schemes, our control method is more practical because the random sampling intervals always happen in some practical situation. In addition, a Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can fully capture the information on stochastic sampling intervals, stochastic input delays, and nonlinear functions. Based on the LKF and Wirtinger’s inequality, less conservative synchronization criteria are obtained. Finally, numerical examples are given to illustrate the effectiveness and superiorities of the proposed results.

New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems

This paper investigates the problem of designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems (CLSs) via a new approach. Specially, first, multiple stochastic sampling intervals with given probabilities are considered and satisfy Bernoulli distribution. Second, unlike other studies, a unified probability framework, which takes sampling interval and time-varying delay into account, is proposed for the first time to design the controller. Based on this unified probability framework, an augmented Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can take full advantage of the available information on actual sampling pattern. Different from some existing LKFs needing to be positive definite on the whole sampling intervals, by the new inequality in Lemma 1, the LKF is positive definite only requiring to be positive definite at sampling times. Third, less conservative synchronization criterion is derived and the desired stochastic sampled-data controller is designed. Finally, numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

Exponential Synchronization of Chaotic Lur’e Systems Using an Adaptive Event-Triggered Mechanism

This paper investigates event-triggered exponential synchronization of master-slave chaotic Lur'e systems (CLSs). First, in order to save communication resources, a novel event-based transmission strategy is developed using continuous-time measurements while a positive minimum inter-event time can be ensured. Second, an adaptive law is adopted to adjust dynamically the event-triggered threshold parameter. Compared with some existing static event-triggered mechanisms, the proposed event-triggered mechanism can provide a better tradeoff between communication resource saving and desired synchronization performance. Third, a switched Lyapunov-Krasovskii functional (LKF) is introduced, which is continuous at the switching instants but not necessarily positive definite at sampling intervals. This LKF is employed to derive a less conservative synchronization criterion for CLSs, based on which, the synchronization controller gain and the event-triggered parameters can be co-designed in terms of linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to illustrate the efficiency of the proposed method.

Event-triggered sampling control for exponential synchronization of chaotic Lur’e systems with time-varying communication delays

This paper investigates the exponential synchronization of chaotic Lur’e systems (CLSs) with time-varying communication delays through event-triggered sampling control. Specially, first, a discrete event-triggered sampling control scheme, which only sends necessary sampling signal through the network, is designed for CLSs. By using this controller, the number of control updates could greatly reduce. Second, by getting utmost out of the usable information on the actual sampling pattern, some new sawtooth structure terms are introduced in the constructed Lyapunov–Krasovskii functional (LKF). It is worth mentioning that, different from some existing results to restrict the LKF to be positive define on the whole sampling intervals, the LKF is positive definite only needing at sampling times thanks to the use of the new inequality in Lemma 1. Third, less conservative synchronization criteria are established and the desired control gain matrix is obtained. Finally, two Chua’s circuit numerical simulations are presented to validate the feasibility and effectiveness of the theoretical results.

Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

SummaryThis paper proposes a novel nonfragile robust asynchronous control scheme for master‐slave uncertain chaotic Lurie network systems with randomly occurring time‐varying parameter uncertainties and controller gain fluctuation. The asynchronous phenomenon occurs between the system modes and the controller modes. In order to consider a more realistic situation in designing a reliable proportional‐derivative controller, Bernoulli stochastic process and memory feedback are introduced to the concept of nonlinear control system. First, by taking full advantage of the additional derivative state term and variable multiple integral terms, a newly augmented Lyapunov‐Krasovskii functional is constructed via an adjustable parameter. Second, based on new integral inequalities including almost all of the existing integral inequalities, which can produce more accurate bounds with more orthogonal polynomials considered, less conservative synchronization criteria are obtained. Third, a desired nonfragile estimator controller is achieved under the aforementioned methods. Finally, 4 numerical simulation examples of Chua's circuit and 3‐cell cellular neural network with multiscroll chaotic attractors are presented to illustrate the effectiveness and advantages of the proposed theoretical results.