Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches

Further Results for Edge Convergence of Directed Signed Networks

The edge convergence problems have been explored for directed signed networks recently in 2019 by Du, Ma, and Meng, of which the analysis results, however, depend heavily on the strong connectivity of the network topologies. The question asked in this article is: whether and how can the edge convergence be achieved when the strong connectivity is not satisfied? The answer for the case of spanning tree is given. It is shown that if a signed network is either structurally balanced or r-structurally unbalanced, then the edge state can be ensured to converge to a constant vector. In contrast, if a signed network is both structurally unbalanced and r-structurally balanced, then its edge state does not converge to a constant vector any longer, but to a time-varying vector trajectory with a constant speed. Further, the dynamic behavior results of edges can be derived to address the node convergence problems of signed networks. The simulation examples are provided to illustrate the validity of the established edge convergence results.

New effective approach to quasi synchronization of coupled heterogeneous complex networks

This short paper addresses quasi synchronization of linearly coupled heterogeneous systems. Similarity and difference between the complete synchronization of linearly coupled homogeneous systems and the quasi synchronization of linearly coupled heterogeneous systems will be revealed.

Secure Communication Based on Quantized Synchronization of Chaotic Neural Networks Under an Event-Triggered Strategy

This article presents a secure communication scheme based on the quantized synchronization of master-slave neural networks under an event-triggered strategy. First, a dynamic event-triggered strategy is proposed based on a quantized output feedback, for which a quantized output feedback controller is formed. Second, theoretical criteria are derived to ensure the bounded synchronization of master-slave neural networks. With these criteria, an explicit upper bound is given for the synchronization error. Sufficient conditions are also provided on the existence of quantized output feedback controllers. A Chua's circuit is chosen to illustrate the effectiveness of our theoretical results. Third, a secure communication scheme is presented based on the synchronization of master-slave neural networks by combining the basic principle of cryptology. Then, a secure image communication is studied to verify the feasibility and security performance of the proposed secure communication scheme. The impact of the quantization level and the event-triggered control (ETC) on image decryption is investigated through experiments.

Adaptive Consensus Control of Linear Multiagent Systems With Dynamic Event-Triggered Strategies

This paper is concerned with event-triggered consensus of general linear multiagent systems (MASs) in leaderless and leader-following networks, respectively, in the framework of adaptive control. A distributed dynamic event-triggered strategy is first proposed, in which an auxiliary parameter is introduced for each agent to regulate its threshold dynamically. The time-varying threshold ensures less triggering instants, compared with the traditional static one. Then under the proposed event-triggered strategy, a distributed adaptive consensus protocol is formed including the updating law of the coupling strength for each agent. Some criteria are derived to guarantee leaderless or leader-following consensus for MASs with general linear dynamics, respectively. Moreover, it is proved that the triggering time sequences do not exhibit Zeno behavior. Finally, the effectiveness of the proposed dynamic event-triggered control mechanism combined with adaptive control is validated by two examples.

Quasi-Synchronization of Discrete-Time Lur'e-Type Switched Systems With Parameter Mismatches and Relaxed PDT Constraints

This paper investigates the problem of quasi-synchronization for a class of discrete-time Lur'e-type switched systems with parameter mismatches and transmission channel noises. Different from the previous studies referring to the persistent dwell-time (PDT) switching signals, the average dwell-time (ADT) constraints combined with the PDT are considered simultaneously in this paper to relax the limitation of dwell-time requirements and to improve the flexibility of the PDT switching signal design. By virtue of the semi-time-varying (STV) Lyapunov function, the synchronization criteria for transmitter-receiver systems in a switched version are obtained to satisfy a prescribed synchronization error bound. An estimate of the synchronization error bound is provided via the reachable set approach and, further, an explicit description of the error bounds is given. Then, sufficient conditions on the existence of STV observers are derived with a predetermined error bound, and the corresponding observer gains are calculated via solving a group of linear matrix inequalities. Finally, the effectiveness and validness of the developed theoretical results are demonstrated via a numerical example.

Projective Synchronization of Delayed Neural Networks With Mismatched Parameters and Impulsive Effects

In this paper, the impulsive effects on projective synchronization between the parameter mismatched neural networks with mixed time-varying delays have been analyzed. Since complete synchronization is not possible due to the existence of parameter mismatch and projective factor, a drive has been taken to achieve the weak projective synchronization of different neural networks under impulsive control strategies. Through the use of matrix measure technique and the extended comparison principle based on the formula of variation of parameters for mixed time-varying delayed impulsive systems, sufficient criteria have been derived for exponential convergence of the networks under the effects of extensive range of impulse. Instead of upper or lower bound of the impulsive interval, the concept of the average impulsive interval is applied to estimate the number of impulsive points in an interval. The concept of calculus is applied for optimizing the synchronization error bounds which are obtained because of different ranges of impulse. Finally, the numerical simulations for various impulsive ranges for different cases are presented graphically to validate the efficiency of the theoretical results.

Synchronization of the Networked System With Continuous and Impulsive Hybrid Communications

Many networked systems display some kind of dynamics behaving in a style with both continuous and impulsive communications. The cooperation behaviors of these networked systems with continuous connected or impulsive connected or both connected topologies of communications are important to understand. This paper is devoted to the synchronization of the networked system with continuous and impulsive hybrid communications, where each topology of communication mode is not connected in every moment. Two kind of structures, i.e., fixed structure and switching structures, are taken into consideration. A general concept of directed spanning tree (DST) is proposed to describe the connectivity of the networked system with hybrid communication modes. The suitable Lyapunov functions are constructed to analyze the synchronization stability. It is showed that for fixed topology having a jointly DST, the networked system with continuous and impulsive hybrid communication modes will achieve asymptotic synchronization if the feedback gain matrix and the average impulsive interval are properly selected. The results are then extended to the switching case where the graph has a frequently jointly DST. Some simple examples are then given to illustrate the derived synchronization criteria.

Passivity Analysis of Delayed Neural Networks Based on Lyapunov-Krasovskii Functionals With Delay-Dependent Matrices

This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov-Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel-Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel-Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

H∞ Synchronization of Networked Master-Slave Oscillators With Delayed Position Data: The Positive Effects of Network-Induced Delays

This paper is concerned with H_∞ synchronization of coupled oscillators in a master-slave framework, in which the oscillators cannot be stabilized by nondelayed sampled position data, but can be stabilized by sampled position data with delays restricted by nonzero lower bounds and upper bounds. A configuration of networked master-slave oscillators with a remote controller is first constructed. Then the positive effects of delays on master-slave synchronization are investigated. Some delay-dependent H_∞ synchronization criteria are derived by constructing augmented discretized Lyapunov-Krasovskii functionals for determinate sampling and stochastic sampling, respectively. The controller can be designed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to verify the theoretical results. It is shown that the maximum allowable sampling period in the case of stochastic sampling is larger than the one in the case of determinate sampling. Stochastic sampling can also provide a tradeoff between network-induced delays and the sampling periods, enhancing the master-slave synchronization performance.

Distributed Impulsive Quasi-Synchronization of Lur'e Networks With Proportional Delay

This paper investigates the exponential synchronization of nonidentically coupled Lur'e dynamical networks with proportional delay. Since the heterogeneities existed in different Lur'e systems, quasi-synchronization rather than complete synchronization is thus discussed. Different from general time delay, the proportional delay is a type of unbounded time-varying delay, which tremendously increases the requirements on network synchronization. Based on distributed impulsive pinning control protocol and different roles that impulsive effects play, the criteria for quasi-synchronization of nonidentically coupled Lur'e dynamical networks are derived by jointly applying the delayed impulsive comparison principle, the extended formula for the variation of parameters, and the definition of an average impulsive interval. Moreover, synchronization errors for different impulsive effects with different functions are evaluated and simultaneously, the corresponding exponential convergence rates are obtained. In addition, three numerical examples are presented to illustrate the validity of the control scheme and the theoretical analysis.

Quasi-Synchronization of Delayed Chaotic Memristive Neural Networks

We study the problem of master-slave synchronization of two delayed memristive neural networks (MNNs). Different from most previous papers, memristors are regarded as uncertain continuous time-varying parameters, and MNNs are modeled by neural networks (NNs) with continuous time-varying parameters and polytopic uncertainty. Thus, synchronization of two delayed MNNs is converted into synchronization of delayed NNs with uncertain parameter mismatches. Quasi-synchronization criteria are derived by Lyapunov function and inequality technique. It is shown that, given a predetermined error bound, quasi-synchronization of two delayed chaotic MNNs can be achieved provided that the pinning strength is larger than a threshold. In the end, a numerical example is provided to illustrate the effectiveness of the derived results.

Admissible Delay Upper Bounds for Global Asymptotic Stability of Neural Networks With Time-Varying Delays

This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov-Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov-Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method.

Hierarchical Type Stability Criteria for Delayed Neural Networks via Canonical Bessel-Legendre Inequalities

This paper is concerned with global asymptotic stability of delayed neural networks. Notice that a Bessel-Legendre inequality plays a key role in deriving less conservative stability criteria for delayed neural networks. However, this inequality is in the form of Legendre polynomials and the integral interval is fixed on . As a result, the application scope of the Bessel-Legendre inequality is limited. This paper aims to develop the Bessel-Legendre inequality method so that less conservative stability criteria are expected. First, by introducing a canonical orthogonal polynomial sequel, a canonical Bessel-Legendre inequality and its affine version are established, which are not explicitly in the form of Legendre polynomials. Moreover, the integral interval is shifted to a general one . Second, by introducing a proper augmented Lyapunov-Krasovskii functional, which is tailored for the canonical Bessel-Legendre inequality, some sufficient conditions on global asymptotic stability are formulated for neural networks with constant delays and neural networks with time-varying delays, respectively. These conditions are proven to have a hierarchical feature: the higher level of hierarchy, the less conservatism of the stability criterion. Finally, three numerical examples are given to illustrate the efficiency of the proposed stability criteria.

Impulsive Effects on Quasi-Synchronization of Neural Networks With Parameter Mismatches and Time-Varying Delay

This paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time-varying delay. Due to the parameter mismatch phenomena existed in neural networks, the problem of quasi-synchronization is thus discussed by applying some impulsive control strategies. Based on the definition of average impulsive interval and the extended comparison principle for impulsive systems, some criteria for achieving the quasi-synchronization of neural networks are derived. More extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization. In addition, according to the extended formula for the variation of parameters with time-varying delay, precisely exponential convergence rates and quasi-synchronization errors are obtained, respectively, in view of different types impulsive effects. Finally, some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis.

Multisynchronization of Coupled Heterogeneous Genetic Oscillator Networks via Partial Impulsive Control

This paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy. The coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties. The definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real. Considering that each genetic oscillator consists of a large number of biochemical molecules, we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization. Not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant. Theoretical analysis of multisynchronization is carried out by the control theory approach, and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established. At last, numerical simulations are exploited to demonstrate the effectiveness of our results.

Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

Cooperative Control of Heterogeneous Uncertain Dynamical Networks: An Adaptive Explicit Synchronization Framework

This paper proposes an adaptive explicit synchronization framework to address the cooperative control for heterogeneous uncertain dynamical networks under switching communication topologies. The main contribution is to develop an adaptive explicit synchronization algorithm, in which the synchronization state can be completely tracked by each agent in real time rather than only be measured after the synchronization process of all agents is over. By introducing appropriate assumptions, a class of adaptive explicit synchronization protocols is designed by using a combination of the virtual leader's states, the neighboring agents' relative information, distributed feedback gain, and distributed average weighted parameters. It is proved in the sense of Lyapunov that, if the dwell time is larger than a positive threshold, the cooperative control problem for the closed-loop heterogeneous uncertain dynamical networks under switching of strongly-connected communication topologies can be solved by the proposed adaptive explicit synchronization algorithm. Furthermore, by assuming that the topology is frequently strongly-connected, it shows that intermittent adaptive explicit synchronization can be achieved with well-designed control parameters. Two examples are presented to demonstrate the effectiveness of the proposed theory.

Leader-Following Consensus of Nonlinear Multiagent Systems With Stochastic Sampling

This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation

This paper proposes a new non-fragile stochastic control method to investigate the robust sampled-data synchronization problem for uncertain chaotic Lurie systems (CLSs) with time-varying delays. The controller gain fluctuation and time-varying uncertain parameters are supposed to be random and satisfy certain Bernoulli distributed white noise sequences. Moreover, by choosing an appropriate Lyapunov-Krasovskii functional (LKF), which takes full advantage of the available information about the actual sampling pattern and the nonlinear condition, a novel synchronization criterion is developed for analyzing the corresponding synchronization error system. Furthermore, based on the most powerful free-matrix-based integral inequality (FMBII), the desired non-fragile sampled-data estimator controller is obtained in terms of the solution of linear matrix inequalities. Finally, three numerical simulation examples of Chua's circuit and neural network are provided to show the effectiveness and superiorities of the proposed theoretical results.

Event-Triggered Distributed Average Consensus Over Directed Digital Networks With Limited Communication Bandwidth

In this paper, we consider the event-triggered distributed average-consensus of discrete-time first-order multiagent systems with limited communication data rate and general directed network topology. In the framework of digital communication network, each agent has a real-valued state but can only exchange finite-bit binary symbolic data sequence with its neighborhood agents at each time step due to the digital communication channels with energy constraints. Novel event-triggered dynamic encoder and decoder for each agent are designed, based on which a distributed control algorithm is proposed. A scheme that selects the number of channel quantization level (number of bits) at each time step is developed, under which all the quantizers in the network are never saturated. The convergence rate of consensus is explicitly characterized, which is related to the scale of network, the maximum degree of nodes, the network structure, the scaling function, the quantization interval, the initial states of agents, the control gain and the event gain. It is also found that under the designed event-triggered protocol, by selecting suitable parameters, for any directed digital network containing a spanning tree, the distributed average consensus can be always achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. Two simulation examples are provided to illustrate the feasibility of presented protocol and the correctness of the theoretical results.

Mean deviation coupling synchronous control for multiple motors via second-order adaptive sliding mode control

A new mean deviation coupling synchronization control strategy is developed for multiple motor control systems, which can guarantee the synchronization performance of multiple motor control systems and reduce complexity of the control structure with the increasing number of motors. The mean deviation coupling synchronization control architecture combining second-order adaptive sliding mode control (SOASMC) approach is proposed, which can improve synchronization control precision of multiple motor control systems and make speed tracking errors, mean speed errors of each motor and speed synchronization errors converge to zero rapidly. The proposed control scheme is robustness to parameter variations and random external disturbances and can alleviate the chattering phenomena. Moreover, an adaptive law is employed to estimate the unknown bound of uncertainty, which is obtained in the sense of Lyapunov stability theorem to minimize the control effort. Performance comparisons with master-slave control, relative coupling control, ring coupling control, conventional PI control and SMC are investigated on a four-motor synchronization control system. Extensive comparative results are given to shown the good performance of the proposed control scheme.

Optimal Communication Network-Based H∞ Quantized Control With Packet Dropouts for a Class of Discrete-Time Neural Networks With Distributed Time Delay

This paper is concerned with optimal communication network-based H∞ quantized control for a discrete-time neural network with distributed time delay. Control of the neural network (plant) is implemented via a communication network. Both quantization and communication network-induced data packet dropouts are considered simultaneously. It is assumed that the plant state signal is quantized by a logarithmic quantizer before transmission, and communication network-induced packet dropouts can be described by a Bernoulli distributed white sequence. A new approach is developed such that controller design can be reduced to the feasibility of linear matrix inequalities, and a desired optimal control gain can be derived in an explicit expression. It is worth pointing out that some new techniques based on a new sector-like expression of quantization errors, and the singular value decomposition of a matrix are developed and employed in the derivation of main results. An illustrative example is presented to show the effectiveness of the obtained results.

Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov-Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.

Hierarchical cooperative control for multiagent systems with switching directed topologies

The hierarchical cooperative control problem is concerned for a two-layer networked multiagent system under switching directed topologies. The group cooperative objective is to achieve finite-time formation control for the upper layer of leaders and containment control for the lower layer of followers. Two kinds of cooperative strategies, including centralized-distributed control and distributed-distributed control, are proposed for two types of switching laws: 1) random switching law with the dwell time and 2) Markov switching law with stationary distribution. Utilizing the state transition matrix methods and matrix measure techniques, some sufficient conditions are derived for asymptotical containment control and exponential almost sure containment control, respectively. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed control schemes.

Local synchronization of chaotic neural networks with sampled-data and saturating actuators

This paper investigates the problem of local synchronization of chaotic neural networks with sampled-data and actuator saturation. A new time-dependent Lyapunov functional is proposed for the synchronization error systems. The advantage of the constructed Lyapunov functional lies in the fact that it is positive definite at sampling times but not necessarily between sampling times, and makes full use of the available information about the actual sampling pattern. A local stability condition of the synchronization error systems is derived, based on which a sampled-data controller with respect to the actuator saturation is designed to ensure that the master neural networks and slave neural networks are locally asymptotically synchronous. Two optimization problems are provided to compute the desired sampled-data controller with the aim of enlarging the set of admissible initial conditions or the admissible sampling upper bound ensuring the local synchronization of the considered chaotic neural networks. A numerical example is used to demonstrate the effectiveness of the proposed design technique.