Class Of Discrete-time Complex Networks Research Articles

Unbiased state and fault estimation for discrete-time complex networks with time delays

In this paper, the joint state and fault estimation problem for a class of discrete-time complex networks with time delays is investigated. The information on the dynamics of the fault is not required with an appropriate structure of the proposed fault estimator. Unbiased state and fault estimation can be obtained simultaneously at each node only with locally available information, thereby avoiding the requirement of a centre node which collects information from every node. Considering the effects of time delays and the interconnections between different nodes, an upper bound of the estimation error covariance is calculated, and the desired filter parameters are obtained in a recursive manner such that the trace of the bound is minimised. The existence conditions of the developed filter are provided explicitly as well. Finally, a simulation example is employed to demonstrate the state estimation and fault diagnosis performances of the given strategy.

Dynamic event-triggered fault estimation for complex networks with time-correlated fading channels

In this paper, the problem of dynamic event-based finite-horizon H∞ fault estimation is studied for a class of discrete-time complex networks with fading channels. In the communication from sensor to estimator, the channel fading phenomenon is considered, which is a dynamic process and reflects the actual situation. Moreover, the dynamic event-triggered mechanism is implemented to schedule the signal transmissions. This paper plans to design a fault estimator to meet the predetermined H∞ performance requirements. First, sufficient conditions are established to ensure the existence of the desired H∞ fault estimator. Then, the gain of the H∞ fault estimator is derived in terms of the solution to a set of recursive matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of our developed fault estimation approach.

State estimate via outputs from the fraction of nodes for discrete-time complex networks with Markovian jumping parameters and measurement noise

This paper deals with the state estimate problem for a class of discrete-time complex networks. The target plant involves Markovian jumping parameters and mode-dependent distributed time-delays. It is assumed that the measurements for the estimate purpose are just from a portion of network nodes, and corrupted by a certain stochastic noise. A unified framework is developed to cope with the state estimation issue based on the outputs from the fraction of nodes for the discrete-time complex networks with distributed time delay and measurement noise. By employing the Lyapunov stability theory and some new techniques, the sufficient conditions are established to ensure the state estimation error is exponentially ultimately mean-square bounded. As the special case when the measurement is noise-free, the resulting criteria are to guarantee that the dynamics of state estimation error is exponentially stable. In addition, the estimator gain matrices are given in the explicit formula. Finally, numerical simulations are presented to illustrate the proposed approach.

Joint State and Fault Estimation of Complex Networks Under Measurement Saturations and Stochastic Nonlinearities

In this paper, the joint state and fault estimation problem is investigated for a class of discrete-time complex networks with measurement saturations and stochastic nonlinearities. The difference between the actual measurement and the saturated measurement is regarded as an unknown input and the system is thus re-organized as a singular system. An appropriate estimator is designed for each node which aims to estimate the system states and the loss of the actuator effectiveness simultaneously. In the presence of measurement saturations and stochastic nonlinearities, upper bounds of the error covariances of the fault estimates are recursively obtained and then minimized. Sufficient conditions are proposed to guarantee the existence, unbiasedness, and boundeness of the developed estimator. Our developed estimator design algorithm is distributed because it depends only on the local information and the information from the neighboring nodes, thereby avoiding the usage of a center estimator. Finally, simulation results are presented to show the performance of the proposed strategy in simultaneously estimating the states and faults.

Matrix projective synchronization for a class of discrete-time complex networks with commonality via controlling the crucial node

This article proposes two control strategies to realize matrix projective synchronization (MPS) for a class of discrete-time complex dynamical networks (DTCDNs). It is worth pointing out that our network model is composed of nodes with different state dimensions and its outer coupling configuration matrix can be asymmetric. In addition, since a small percentage of nodes that play more important role than others usually exist in a network, thus, one important node, which is named as crucial node in this paper, is taken into account in our network model. Besides, the commonality between each node and the crucial node is also precisely expressed. Further, based on the crucial node and the commonality and associated with the Lyapunov stability theory, two control strategies are addressed to realize the exponential matrix projective synchronization (EMPS) and asymptotic matrix projective synchronization (AMPS), respectively. It should be stressed that only the crucial node is controlled and only the state of the crucial node is applied to design the EMPS and AMPS controllers. This is promising to reduce the control cost as much as possible and to improve the feasibility of our MPS strategies. The effectiveness and feasibility of our MPS schemes are rigorously proved in theory as well as verified by two numerical examples.

Partial-Nodes-Based State Estimation for Complex Networks With Constrained Bit Rate

In this paper, the partial-nodes-based (PNB) state estimation issue is investigated for a class of discrete-time complex networks with constrained bit rate and bounded noises. Measurements from only a fraction of nodes in a complex network are acquired and used for state estimation. The communication between sensor nodes and estimators is accomplished over a wireless digital communication network with limited bandwidth. A bit rate constraint model is introduced to reflect the bandwidth allocation rules of partially accessible nodes. A sufficient condition is proposed under which the PNB state estimation error system is guaranteed to be ultimately bounded, and then a bit rate condition assuring a specific estimation performance is presented. The estimator gains are derived by solving two optimization problems in order to ensure two estimation performance metrics (i.e. the smallest ultimate bound and the fastest decay rate). Furthermore, the co-design issue of the bit rate allocation protocol and the estimator gains is addressed by means of particle swarm optimization and linear matrix inequalities. Finally, three numerical simulations are provided to verify the validity of the proposed PNB state estimation approach.

Input–Output Finite-Time Estimation for Complex Networks With Switching Topology Under Dynamic Event-Triggered Transmission

This article investigates the problem of input-output finite-time estimation for a class of discrete-time complex networks with switching topology. The dynamic event-triggered communication manner is proposed to conduct the data transmission of the switching signal and measurement outputs subject to random sensor nonlinearities. The asynchronism of the switching and triggering actions also leads to the received switching index by the designed estimator being inconsistent with that of the estimated switched complex networks. Then, a novel piecewise Lyapunov functional, which is proved to be less conservative than the general one, is then constructed for handling the input-output finite-time estimation under the unmatched circumstance. Sufficient conditions are formulated to ensure that the underlying estimation error systems are input-output finite-time stochastically stable with respect to the norm bounded inputs within a finite time. Finally, the superiority and applicability of the developed approach are verified by a simulation example.

Scalable Distributed Filtering for a Class of Discrete-Time Complex Networks Over Time-Varying Topology.

This article is concerned with the distributed filtering problem for a class of discrete complex networks over time-varying topology described by a sequence of variables. In the developed scalable filtering algorithm, only the local information and the information from the neighboring nodes are used. As such, the proposed filter can be implemented in a truly distributed manner at each node, and it is no longer necessary to have a certain center node collecting information from all the nodes. The aim of the addressed filtering problem is to design a time-varying filter for each node such that an upper bound of the filtering error covariance is ensured and the desired filter gain is then calculated by minimizing the obtained upper bound. The filter is established by solving two sets of recursive matrix equations, and thus, the algorithm is suitable for online application. Sufficient conditions are provided under which the filtering error is exponentially bounded in mean square. The monotonicity of the filtering error with respect to the coupling strength is discussed as well. Finally, an illustrative example is presented to demonstrate the feasibility and effectiveness of our distributed filtering strategy.

A Partial-Nodes-Based Information fusion approach to state estimation for discrete-Time delayed stochastic complex networks

This paper is concerned with the information-fusion-based state estimation problem for a class of discrete-time complex networks with time-varying delays and stochastic perturbations. The measurement outputs available for state estimation are from a fraction of network nodes, and the addressed problem is therefore referred to as the so-called Partial-Nodes-Based (PNB) state estimation problem. By employing the Lyapunov stability theory, a novel framework is established to cope with the PNB state estimation problem by the measurement outputs collected from partial network nodes. By constructing specific Lyapunov-Krasovskii functionals, sufficient criteria are derived for the existence of the desired exponentially ultimately bounded state estimator in mean square for the complex networks. Moreover, a special case is considered where the complex network under investigation is free of stochastic perturbations and the corresponding analysis issue is discussed to ensure the existence of an exponential state estimator. In addition, the explicit expressions of the gains of the desired estimators are characterized. Finally, a numerical illustrative example is presented to demonstrate the effectiveness of the obtained theoretical results.

Recursive filtering for complex networks using non‐linearly coupled UKF

This study is concerned with the recursive filtering problem for a class of discrete-time complex networks with non-linearly coupled terms. A coupled unscented Kalman filter (UKF) is developed, where the sigma points of the UKF are propagated by introducing the coupled terms. By using the stochastic analysis technique, a sufficient condition is established to guarantee the boundedness of the estimation errors, where an upper bound for the coupling strength is derived. It is shown that the upper bound of the coupling strength is inversely proportional to the number of nodes. A numerical example involving tracking of multiple interacting targets is provided to verify the effectiveness of the proposed filter.

State estimation for complex networks with randomly occurring coupling delays

In this paper, the H∞ state estimation problem is investigated for a class of discrete-time complex networks with randomly occurring phenomena. The proposed randomly occurring phenomena include both probabilistic missing measurements and randomly occurring coupling delays which are described by two random variable sequences satisfying individual probability distributions, respectively. Rather than the common Lipschitz-type function, a more general sector-like nonlinear function is employed to characterize the nonlinearities in the networks. The purpose of the addressed H∞ state estimation problem is to design a state estimator such that, for all admissible nonlinear disturbances, missing measurements as well as coupling delays, the dynamics of the augmented systems is guaranteed to be exponentially mean-square stable and attenuated to a given H∞ performance level. By constructing a novel Lyapunov–Krasovskii functional and utilizing convex optimization method as well as Kronecker product, we derive the sufficient conditions under which the desired state estimator exists. An illustrative example is exploited to show the effectiveness of the proposed state estimation scheme.

ON SYNCHRONIZATION OF DISCRETE-TIME MARKOVIAN JUMPING STOCHASTIC COMPLEX NETWORKS WITH MODE-DEPENDENT MIXED TIME-DELAYS

In this paper, the synchronization problem is investigated for a new class of discrete-time complex networks. Such complex networks involve the Markovian jumping parameters, mode-dependent discrete and distributed time-delays, constant and delayed couplings, as well as multiple stochastic disturbances. The stochastic disturbances influence the constant coupling term, the delayed coupling term, as well as the overall network dynamics, which could better describe the dynamical behavior of a coupled complex network presented within a noisy environment. With help from the Lyapunov functional method and the properties of Kronecker product, we employ the stochastic analysis techniques to derive several delay-dependent sufficient conditions under which the coupled complex network is asymptotically synchronized in the mean square. The criteria obtained in this paper are in the form of LMIs whose solution can be easily calculated using the standard numerical software. It is shown that our main results can cover many existing ones reported in the literature. A numerical example is presented to illustrate the usefulness of our results.