Event-Triggered State Estimation for Complex Networks With Mixed Time Delays via Sampled Data Information: The Continuous-Time Case

In this paper, the event-triggered state estimation problem is investigated for a class of complex networks with mixed time delays using sampled data information. A novel state estimator is presented to estimate the network states. A new event-triggered transmission scheme is proposed to reduce unnecessary network traffic between the sensors and the estimator, where the sampled data is transmitted to the estimator only when the so-called "event-triggered condition" is satisfied. The purpose of the problem addressed is to design an estimator for the complex network such that the estimation error is ultimately bounded in mean square. By utilizing Lyapunov theory combined with the stochastic analysis approach, sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square. Then, the desired estimator gain matrices are obtained via solving a convex problem. Finally, a numerical example is given to illustrate the effectiveness of the results.

An Integrated Approach to Global Synchronization and State Estimation for Nonlinear Singularly Perturbed Complex Networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both "slow" and "fast" dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable.

Exponential synchronization of complex networks of linear systems and nonlinear oscillators: a unified analysis

A unified approach to the analysis of synchronization for complex dynamical networks, i.e., networks of partial-state coupled linear systems and networks of full-state coupled nonlinear oscillators, is introduced. It is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks, thus making it feasible to consider the error dynamics for the whole network system. Different from the other various methods given in the existing literature, the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form, but also explicitly specifying the convergence rate.

Synchronization control for stochastic neural networks with mixed time-varying delays

Synchronization control of stochastic neural networks with time-varying discrete and continuous delays has been investigated. A novel control scheme is proposed using the Lyapunov functional method and linear matrix inequality (LMI) approach. Sufficient conditions have been derived to ensure the global asymptotical mean-square stability for the error system, and thus the drive system synchronizes with the response system. Also, the control gain matrix can be obtained. With these effective methods, synchronization can be achieved. Simulation results are presented to show the effectiveness of the theoretical results.

Robust H∞ filtering for a class of complex networks with stochastic packet dropouts and time delays

The robust H_∞ filtering problem is investigated for a class of complex network systems which has stochastic packet dropouts and time delays, combined with disturbance inputs. The packet dropout phenomenon occurs in a random way and the occurrence probability for each measurement output node is governed by an individual random variable. Besides, the time delay phenomenon is assumed to occur in a nonlinear vector-valued function. We aim to design a filter such that the estimation error converges to zero exponentially in the mean square, while the disturbance rejection attenuation is constrained to a given level by means of the H_∞ performance index. By constructing the proper Lyapunov-Krasovskii functional, we acquire sufficient conditions to guarantee the stability of the state detection observer for the discrete systems, and the observer gain is also derived by solving linear matrix inequalities. Finally, an illustrative example is provided to show the usefulness and effectiveness of the proposed design method.

H ∞ cluster synchronization for a class of neutral complex dynamical networks with Markovian switching

H_∞ cluster synchronization problem for a class of neutral complex dynamical networks (NCDNs) with Markovian switching is investigated in this paper. Both the retarded and neutral delays are considered to be interval mode dependent and time varying. The concept of H_∞ cluster synchronization is proposed to quantify the attenuation level of synchronization error dynamics against the exogenous disturbance of the NCDNs. Based on a novel Lyapunov functional, by employing some integral inequalities and the nature of convex combination, mode delay-range-dependent H_∞ cluster synchronization criteria are derived in the form of linear matrix inequalities which depend not only on the disturbance attenuation but also on the initial values of the NCDNs. Finally, numerical examples are given to demonstrate the feasibility and effectiveness of the proposed theoretical results.

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.

H∞ state estimation for complex networks with uncertain inner coupling and incomplete measurements

In this paper, the H∞ state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements. With the aid of the interval matrix approach, we make the first attempt to characterize the uncertainties entering into the inner coupling matrix. The incomplete measurements under consideration include sensor saturations, quantization, and missing measurements, all of which are assumed to occur randomly. By introducing a stochastic Kronecker delta function, these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability. With the measurement model, a set of H∞ state estimators is designed such that, for all admissible incomplete measurements as well as the uncertain coupling strength, the estimation error dynamics is exponentially mean-square stable and the H∞ performance requirement is satisfied. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.

Coordination of multiagents interacting under independent position and velocity topologies

We consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs. Different algorithms are proposed and analyzed for different settings, including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies, as well as the case with a group velocity reference signal under switching velocity interaction. It is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions. Such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify. Rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory, matrix analysis as well as the Lyapunov stability theory.

Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay

This paper studies the problem of sampled-data exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and uncertain sampling. By combining the time-dependent Lyapunov functional approach and convex combination technique, a criterion is derived to ensure the exponential stability of the error dynamics, which fully utilizes the available information about the actual sampling pattern. Based on the derived condition, the design method of the desired sampled-data controllers is proposed to make the CDNs exponentially synchronized and obtain a lower-bound estimation of the largest sampling interval. Simulation examples demonstrate that the presented method can significantly reduce the conservatism of the existing results, and lead to wider applications.

Exponential H∞ synchronization and state estimation for chaotic systems via a unified model

In this paper, H∞ synchronization and state estimation problems are considered for different types of chaotic systems. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems, such as Hopfield neural networks, cellular neural networks, Chua's circuits, unified chaotic systems, Qi systems, chaotic recurrent multilayer perceptrons, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal H∞ norm constraint. The state estimation problem is then studied for the same unified model, where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level. The parameters of these controllers and filters are obtained by solving the eigenvalue problem. Most chaotic systems can be transformed into this unified model, and H∞ synchronization controllers and state estimators for these systems are designed in a unified way. Three numerical examples are provided to show the usefulness of the proposed H∞ synchronization and state estimation conditions.

Complete synchronization of temporal Boolean networks

This letter studies complete synchronization of two temporal Boolean networks coupled in the drive-response configuration. Necessary and sufficient conditions are provided based on the algebraic representation of Boolean networks. Moreover, the upper bound to check the criterion is given. Finally, an illustrative example shows the efficiency of the proposed results.

Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization

This paper deals with a class of complex networks with nonideal coupling networks, and addresses the problem of asymptotic synchronization of the complex network through designing adaptive pinning control and coupling adjustment strategies. A more general coupled nonlinearity is considered as perturbations of the network, while a serious faulty network named deteriorated network is also proposed to be further study. For the sake of eliminating these adverse impacts for synchronization, indirect adaptive schemes are designed to construct controllers and adjusters on pinned nodes and nonuniform couplings of un-pinned nodes, respectively. According to Lyapunov stability theory, the proposed adaptive strategies are successful in ensuring the achievement of asymptotic synchronization of the complex network even in the presence of perturbed and deteriorated networks. The proposed schemes are physically implemented by circuitries and tested by simulation on a Chua's circuit network.

Robust synchronization for 2-D discrete-time coupled dynamical networks

In this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini-Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.

Global stability of complex-valued recurrent neural networks with time-delays

Since the last decade, several complex-valued neural networks have been developed and applied in various research areas. As an extension of real-valued recurrent neural networks, complex-valued recurrent neural networks use complex-valued states, connection weights, or activation functions with much more complicated properties than real-valued ones. This paper presents several sufficient conditions derived to ascertain the existence of unique equilibrium, global asymptotic stability, and global exponential stability of delayed complex-valued recurrent neural networks with two classes of complex-valued activation functions. Simulation results of three numerical examples are also delineated to substantiate the effectiveness of the theoretical results.

Complete synchronization of Boolean networks

We examine complete synchronization of two deterministic Boolean networks (BNs) coupled unidirectionally in the drive-response configuration. A necessary and sufficient criterion is presented in terms of algebraic representations of BNs. As a consequence, we show that complete synchronization can occur only between two conditionally identical BNs when the transition matrix of the drive network is nonsingular. Two examples are worked out to illustrate the obtained results.

H∞ state estimation for discrete-time complex networks with randomly occurring sensor saturations and randomly varying sensor delays

In this paper, the state estimation problem is investigated for a class of discrete time-delay nonlinear complex networks with randomly occurring phenomena from sensor measurements. The randomly occurring phenomena include randomly occurring sensor saturations (ROSSs) and randomly varying sensor delays (RVSDs) that result typically from networked environments. A novel sensor model is proposed to describe the ROSSs and the RVSDs within a unified framework via two sets of Bernoulli-distributed white sequences with known conditional probabilities. Rather than employing the commonly used Lipschitz-type function, a more general sector-like nonlinear function is used to describe the nonlinearities existing in the network. The purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that, for all probabilistic sensor saturations and sensor delays, the dynamics of the estimation error is guaranteed to be exponentially mean-square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an H∞-norm. In terms of a novel Lyapunov-Krasovskii functional and the Kronecker product, sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method. A simulation example is provided to show the usefulness of the proposed state estimation conditions.

H∞ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model

This paper is concerned with the problem of state estimation for a class of discrete-time chaotic systems with or without time delays. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these systems, such as chaotic neural networks, Chua's circuits, Hénon map, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, H∞ state estimator are designed for this model with sensors to guarantee the asymptotic stability of the estimation error dynamic systems and to reduce the influence of noise on the estimation error. The parameters of these filters are obtained by solving the eigenvalue problem. As most discrete-time chaotic systems with or without time delays can be described with this unified model, H∞ state estimator design for these systems can be done in a unified way. Three numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.

Synchronization control for nonlinear stochastic dynamical networks: pinning impulsive strategy

In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of state-coupled dynamical networks. We will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks. Some generic mean square stability criteria are derived in terms of algebraic conditions, which guarantee that the whole state-coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes. An effective method is given to select the nodes which should be controlled at each impulsive constants. The proportion of the controlled nodes guaranteeing the stability is explicitly obtained, and the synchronization region is also derived and clearly plotted. Numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper.