An Event-Triggered Approach to State Estimation for a Class of Complex Networks With Mixed Time Delays and Nonlinearities

State Estimation of Switched Time-Delay Complex Networks With Strict Decreasing LKF

State estimation issue is investigated for a switched complex network (CN) with time delay and external disturbances. The considered model is general with a one-sided Lipschitz (OSL) nonlinear term, which is less conservative than Lipschitz one and has wide applications. Adaptive mode-dependent nonidentical event-triggered control (ETC) mechanisms for only partial nodes are proposed for state estimators, which are not only more practical and flexible but also reduce the conservatism of the results. By using dwell-time (DT) segmentation and convex combination methods, a novel discretized Lyapunov-Krasovskii functional (LKF) is developed such that the value of LKF at switching instants is strict monotone decreasing, which makes it easy for nonweighted L2 -gain analysis without additional conservative transformation. The main results are given in the form of linear matrix inequalities (LMIs), by which the control gains of the state estimator are designed. A numerical example is given to illustrate the advantages of the novel analytical method.

Event-Triggered Resilient Filtering With the Interval Type Uncertainty for Markov Jump Systems

The problem of event-triggered resilient filtering for Markov jump systems is investigated in this article. The hidden Markov model is used to characterize asynchronous constraints between the filters and the systems. Gain uncertainties of the resilient filter are the interval type in this article, which is more accurate than the norm-bounded type to model the uncertain phenomenon. The number of linear matrix inequalities constraints can be decreased significantly by separating the vertices of the uncertain interval, so that the difficulty of calculation and calculation time can be reduced. Moreover, the event-triggered scheme is applied to depress the consumption of network resources. In order to find a balance between reducing bandwidth consumed and improving system performance, the threshold parameter is designed as a diagonal matrix in the event-triggered scheme. Utilizing the convex optimization method, the sufficient conditions are derived to guarantee that the filtering error systems are stochastically stable and satisfy the extended dissipation performance. Finally, a single-link robot arm system is delivered to certify the effectiveness and advantages of the proposed method.

Distributed Extended State Estimation for Complex Networks With Nonlinear Uncertainty

This article studies the distributed state estimation issue for complex networks with nonlinear uncertainty. The extended state approach is used to deal with the nonlinear uncertainty. The distributed state predictor is designed based on the extended state system model, and the distributed state estimator is designed by using the measurement of the corresponding node. The prediction error and the estimation error are derived. The prediction error covariance (PEC) is obtained in terms of the recursive Riccati equation, and the upper bound of the PEC is minimized by designing an optimal estimator gain. With the vectorization approach, a sufficient condition concerning stability of the upper bound is developed. Finally, a numerical example is presented to illustrate the effectiveness of the designed extended state estimator.

Distributed Filtering for Semi-Markov-Type Sensor Networks With Hybrid Sojourn-Time Distributions-A Nonmonotonic Approach

This article examines the distributed filtering problem for a general class of filtering systems consisting of distributed time-delayed plant and filtering networks with semi-Markov-type topology switching (SMTTS). The SMTTS implies the topology sojourn time can be a hybrid function of different types of probabilistic distributions, typically, binomial distribution used to model unreliable communication links between the filtering nodes and Weibull distribution employed to depict the cumulative abrasion failure. First, by properly constructing a sojourn-time-dependent Lyapunov-Krasovski function (STDLKF), both time-varying topology-dependent filter and topology-dependent filter are designed. Second, a novel nonmonotonic approach with less design conservatism is developed by relaxing the monotonic requirement of STDLKF within each topology sojourn time. Moreover, an algorithm with less computational effort is proposed to generate a semi-Markov chain from a given Markov renewal chain. Simulation examples, including a microgrid islanded system, are presented to testify the generality and elucidate the practical potential of the nonmonotonic approach.

Event-Triggered Control for Markov Jump Systems Subject to Mismatched Modes and Strict Dissipativity

In order to save network resources of discrete-time Markov jump systems, an event-triggered control framework is employed in this article. The threshold parameter in the event-triggered mechanism is designed as a diagonal matrix in which all elements can be adjusted according to system performance requirements. The hidden Markov model is introduced to characterize the asynchronization between the controller and controlled system. The effect of randomly occurring gain fluctuations is taken into account during the controller design. For the purpose of guaranteeing that the closed-loop system is stochastically stable and satisfies the strictly (D₁,D₂,D₃)-γ- dissipative performance, sufficient conditions are constructed by employing the Lyapunov function and stochastic analysis. After linearization, the proposed controller gains are obtained by solving the linear matrix inequalities. Ultimately, a practical example of the dc motor device is used to illustrate the effectiveness of the proposed new design technique.

Event-Triggered Recursive State Estimation for Stochastic Complex Dynamical Networks Under Hybrid Attacks

In this article, the event-based recursive state estimation problem is investigated for a class of stochastic complex dynamical networks under cyberattacks. A hybrid cyberattack model is introduced to take into account both the randomly occurring deception attack and the randomly occurring denial-of-service attack. For the sake of reducing the transmission rate and mitigating the network burden, the event-triggered mechanism is employed under which the measurement output is transmitted to the estimator only when a preset condition is satisfied. An upper bound on the estimation error covariance on each node is first derived through solving two coupled Riccati-like difference equations. Then, the desired estimator gain matrix is recursively acquired that minimizes such an upper bound. Using the stochastic analysis theory, the estimation error is proven to be stochastically bounded with probability 1. Finally, an illustrative example is provided to verify the effectiveness of the developed estimator design method.

Delay Compensation-Based State Estimation for Time-Varying Complex Networks With Incomplete Observations and Dynamical Bias

In this article, a delay-compensation-based state estimation (DCBSE) method is given for a class of discrete time-varying complex networks (DTVCNs) subject to network-induced incomplete observations (NIIOs) and dynamical bias. The NIIOs include the communication delays and fading observations, where the fading observations are modeled by a set of mutually independent random variables. Moreover, the possible bias is taken into account, which is depicted by a dynamical equation. A predictive scheme is proposed to compensate for the influences induced by the communication delays, where the predictive-based estimation mechanism is adopted to replace the delayed estimation transmissions. This article focuses on the problems of estimation method design and performance discussions for addressed DTVCNs with NIIOs and dynamical bias. In particular, a new distributed state estimation approach is presented, where a locally minimized upper bound is obtained for the estimation error covariance matrix and a recursive way is designed to determine the estimator gain matrix. Furthermore, the performance evaluation criteria regarding the monotonicity are proposed from the analytic perspective. Finally, some experimental comparisons are proposed to show the validity and advantages of the new DCBSE approach.

Finite-Time H∞ State Estimation for Two-Time-Scale Complex Networks Under Stochastic Communication Protocol

The issue of finite-time H_∞ state estimation is studied for a class of discrete-time nonlinear two-time-scale complex networks (TTSCNs) whose measurement outputs are transmitted to a remote estimator via a bandwidth-limited communication network under the stochastic communication protocol (SCP). To reflect different time scales of state evolutions, a new discrete-time TTSCN model is devised by introducing a singular perturbation parameter (SPP). For the sake of avoiding/alleviating the undesirable data collisions, the SCP is adopted to schedule the data transmissions, where the transition probabilities involved are assumed to be partially unknown. By constructing a new Lyapunov function dependent on the information of the SCP and SPP, a sufficient condition is derived which ensures that the resulting error dynamics is stochastically finite-time bounded and satisfies a prescribed H_∞ performance index. By resorting to the solutions of several matrix inequalities, the gain matrices of the state estimator are given and the admissible upper bound of the SPP can be evaluated simultaneously. The performance of the designed state estimator is demonstrated by two examples.

Fault-Tolerant Optimal Control for Discrete-Time Nonlinear System Subjected to Input Saturation: A Dynamic Event-Triggered Approach

This paper investigates the dynamic event-triggered fault-tolerant optimal control strategy for a class of output feedback nonlinear discrete-time systems subject to actuator faults and input saturations. To save the communication resources between the sensor and the controller, the so-called dynamic event-triggered mechanism is adopted to schedule the measurement signal. A neural network-based observer is first designed to provide both the system states and fault information. Then, with consideration of the actuator saturation phenomenon, the adaptive dynamic programming (ADP) algorithm is designed based on the estimates provided by the observer. To reduce the computational burden, the optimal control strategy is implemented via the single network adaptive critic architecture. The sufficient conditions are provided to guarantee the boundedness of the overall closed-loop systems. Finally, the numerical simulations on a two-link flexible manipulator system are provided to verify the validity of the proposed control strategy.

Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations

This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the l₂ - l_∞ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the l₂ - l_∞ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

An Event-Triggering Approach to Recursive Filtering for Complex Networks With State Saturations and Random Coupling Strengths

In this article, the recursive filtering problem is investigated for a class of time-varying complex networks with state saturations and random coupling strengths under an event-triggering transmission mechanism. The coupled strengths among nodes are characterized by a set of random variables obeying the uniform distribution. The event-triggering scheme is employed to mitigate the network data transmission burden. The purpose of the problem addressed is to design a recursive filter such that in the presence of the state saturations, event-triggering communication mechanism, and random coupling strengths, certain locally optimized upper bound is guaranteed on the filtering error covariance. By using the stochastic analysis technique, an upper bound on the filtering error covariance is first derived via the solution to a set of matrix difference equations. Next, the obtained upper bound is minimized by properly parameterizing the filter parameters. Subsequently, the boundedness issue of the filtering error covariance is studied. Finally, two numerical simulation examples are provided to illustrate the effectiveness of the proposed algorithm.

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.

Robust Partial-Nodes-Based State Estimation for Complex Networks Under Deception Attacks

In this paper, the partial-nodes-based state estimators (PNBSEs) are designed for a class of uncertain complex networks subject to finite-distributed delays, stochastic disturbances, as well as randomly occurring deception attacks (RODAs). In consideration of the likely unavailability of the output signals in harsh environments from certain network nodes, only partial measurements are utilized to accomplish the state estimation task for the addressed complex network with norm-bounded uncertainties in both the network parameters and the inner couplings. The RODAs are taken into account to reflect the compromised data transmissions in cyber security. We aim to derive the gain parameters of the estimators such that the overall estimation error dynamics satisfies the specified security constraint in the simultaneous presence of stochastic disturbances and deception signals. Through intensive stochastic analysis, sufficient conditions are obtained to guarantee the desired security performance for the PNBSEs, based on which the estimator gains are acquired by solving certain matrix inequalities with nonlinear constraints. A simulation study is carried out to testify the security performance of the presented state estimation method.

Near-Optimal Resilient Control Strategy Design for State-Saturated Networked Systems Under Stochastic Communication Protocol

In this paper, the near-optimal resilient control strategy design problem is investigated for a class of discrete time-varying system in simultaneous presence of stochastic communication protocols (SCPs), gain perturbations, state saturations, and additive nonlinearities. In the sensor-to-controller network, only one sensor is permitted to get access to the communication media so as to avoid possible data collisions. Described by a Markov chain, the SCP is employed to determine which sensor should obtain the access to the network at a certain time. Furthermore, two kinds of well-recognized complexities (i.e., state saturations and additive nonlinearities) are considered in the system model and the phenomenon of controller gain perturbation is also taken into special consideration. Accordingly, the resilient control strategy is designed by: 1) deriving a certain upper bound on the associate cost function of underlying systems and 2) minimizing such an upper bound through the utilization of the completing-the-square technique and the Moore-Penrose pseudo inverse. The resilient control strategy is obtained in an iterative manner by solving a set of coupled backward Riccati-like recursions. Furthermore, based on the proposed control strategies, the infinite horizon case is considered and the corresponding upper bound of the cost function is explicitly provided. Finally, numerical simulations are carried out on power systems in order to verify the validity of the proposed resilient control algorithms.

Resilient State Estimation for 2-D Time-Varying Systems With Redundant Channels: A Variance-Constrained Approach

This paper investigates the state estimation problem for a class of 2-D time-varying systems with error variance constraints, where the implemented estimator gain is subject to stochastic perturbations. Redundant channels are utilized as a protocol to strengthen the transmission reliability and the channels' packet dropout rates are described by mutually uncorrelated Bernoulli distributions. The objective of the addressed problem is to design a resilient estimator such that an upper bound on the estimation error variance is first guaranteed and then minimized at each time step, where the considered gain perturbations are characterized by their statistical properties. By employing the induction method and the variance-constrained approach, an upper bound on the estimation error variance is first constructed by means of the solutions to two Riccati-like difference equations and, subsequently, a locally minimal upper bound is achieved by appropriately designing the gain parameter. Then, an effective algorithm is proposed for designing the desired estimator, which is in a recursive form suitable for online applications. Finally, a numerical simulation is provided to demonstrate the usefulness of the proposed estimation scheme.

Observer-Based Event-Triggered Control for Nonlinear Systems With Mixed Delays and Disturbances: The Input-to-State Stability

In this paper, the input-to-state stabilization problem is investigated for a class of nonlinear delayed systems with exogenous disturbances. The model under consideration is general that covers for both mixed time-delays and Lipschitz-type nonlinearities. An observer-based controller is designed such that the closed-loop system is stable under an event-triggered mechanism. Two separate event-triggered strategies are proposed in sensor-to-observer (S/O) and controller-to-actuator (C/A) channels, respectively, in order to reduce the updating frequencies of the sensor and the controller with guaranteed performance requirements. The notion of input-to-state practical stability is introduced to characterize the performance of the controlled system that caters for the influence from both disturbances and event-triggered schemes. The estimates of the upper bounds of the delayed states and two measurement errors are employed to analyze and further exclude the Zeno behavior resulting from the proposed event-triggered schemes in S/O and C/A channels. The controller gain matrices and the event-trigger parameters are co-designed in terms of the feasibility of certain matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of theoretical results.

Synchronization Control for A Class of Discrete Time-Delay Complex Dynamical Networks: A Dynamic Event-Triggered Approach

This paper is concerned with the synchronization control problem for a class of discrete time-delay complex dynamical networks under a dynamic event-triggered mechanism. For the efficiency of energy utilization, we make the first attempt to introduce a dynamic event-triggering strategy into the design of synchronization controllers for complex dynamical networks. A new discrete-time version of the dynamic event-triggering mechanism is proposed in terms of the absolute errors between control input updates. By constructing an appropriate Lyapunov functional, the dynamics of each network node combined with the introduced event-triggering mechanism are first analyzed, and a sufficient condition is then provided under which the synchronization error dynamics is exponentially ultimately bounded. Subsequently, a set of the desired synchronization controllers is designed by solving a matrix inequality. Finally, a simulation example is provided to verify the effectiveness of the proposed dynamic event-triggered synchronization control scheme.

Exponential Synchronization for Delayed Dynamical Networks via Intermittent Control: Dealing With Actuator Saturations

Over the past two decades, the synchronization problem for dynamical networks has drawn significant attention due to its clear practical insight in biological systems, social networks, and neuroscience. In the case where a dynamical network cannot achieve the synchronization by itself, the feedback controller should be added to drive the network toward a desired orbit. On the other hand, the time delays may often occur in the nodes or the couplings of a dynamical network, and the existence of time delays may induce some undesirable dynamics or even instability. Moreover, in the course of implementing a feedback controller, the inevitable actuator limitations could downgrade the system performance and, in the worst case, destabilize the closed-loop dynamics. The main purpose of this paper is to consider the synchronization problem for a class of delayed dynamical networks with actuator saturations. Each node of the dynamical network is described by a nonlinear system with a time-varying delay and the intermittent control strategy is proposed. By using a combination of novel sector conditions, piecewise Lyapunov-like functionals and the switched system approach, delay-dependent sufficient conditions are first obtained under which the dynamical network is locally exponentially synchronized. Then, the explicit characterization of the controller gains is established by means of the feasibility of certain matrix inequalities. Furthermore, optimization problems are formulated in order to acquire a larger estimate of the set of initial conditions for the evolution of the error dynamics when designing the intermittent controller. Finally, two examples are given to show the benefits and effectiveness of the developed theoretical results.

Remote Nonlinear State Estimation With Stochastic Event-Triggered Sensor Schedule

This paper concentrates on the remote state estimation problem for nonlinear systems over a communication-limited wireless sensor network. Because of the non-Gaussian property caused by nonlinear transformation, the unscented transformation technique is exploited to obtain approximate Gaussian probability distributions of state and measurement. To reduce excessive data transmission, uncontrollable and controllable stochastic event-triggered scheduling schemes are developed to decide whether the current measurement should be transmitted. Compared with some existing deterministic event-triggered scheduling schemes, the newly developed ones possess a potential superiority in maintaining Gaussian property of innovation process. Under the proposed schemes, two nonlinear state estimators are designed based on the unscented Kalman filter. Stability and convergence conditions of these two estimators are established by analyzing behaviors of estimation error and error covariance. It is shown that an expected compromise between communication rate and estimation quality can be achieved by properly tuning event-triggered parameter matrix. Numerical examples are provided to testify the validity of the proposed results.

Quantizer-Based Triggered Control for Chaotic Synchronization With Information Constraints

This paper mainly focuses on synchronization of controlled drive-response systems under Lurie form through a limited channel. The main contribution of this paper is the quantizer-based triggered methodology proposed based on three coders. By exploring coder structure information and fusing quantization and trigger errors together, this strategy can reduce transmission burden while increase synchronization speed concurrently. And the final synchronization error can be bounded within a predetermined fixed value. According to the initial output of drive system, different coders are purposely designed. With the proposed trigger schemes, traditional binary coder with memory cannot achieve desired performance. Meanwhile, it is found that the static coder leads to satisfactory performance when initial drive system output is within limited region. Combining the advantages of the above two coders, a mixed coder is designed to overcome the shortcomings. Moreover, synchronization error and transmission bit rate are thoroughly discussed and Zeno behavior is radically prevented. Finally, simulations for two Chua's circuits are given to illustrate the validity of the proposed method.

Synchronization Control for a Class of Discrete-Time Dynamical Networks With Packet Dropouts: A Coding-Decoding-Based Approach

The synchronization control problem is investigated for a class of discrete-time dynamical networks with packet dropouts via a coding-decoding-based approach. The data is transmitted through digital communication channels and only the sequence of finite coded signals is sent to the controller. A series of mutually independent Bernoulli distributed random variables is utilized to model the packet dropout phenomenon occurring in the transmissions of coded signals. The purpose of the addressed synchronization control problem is to design a suitable coding-decoding procedure for each node, based on which an efficient decoder-based control protocol is developed to guarantee that the closed-loop network achieves the desired synchronization performance. By applying a modified uniform quantization approach and the Kronecker product technique, criteria for ensuring the detectability of the dynamical network are established by means of the size of the coding alphabet, the coding period and the probability information of packet dropouts. Subsequently, by resorting to the input-to-state stability theory, the desired controller parameter is obtained in terms of the solutions to a certain set of inequality constraints which can be solved effectively via available software packages. Finally, two simulation examples are provided to demonstrate the effectiveness of the obtained results.

Event-Triggered State Estimation for Delayed Stochastic Memristive Neural Networks With Missing Measurements: The Discrete Time Case

In this paper, the event-triggered state estimation problem is investigated for a class of discrete-time stochastic memristive neural networks (DSMNNs) with time-varying delays and missing measurements. The DSMNN is subject to both the additive deterministic disturbances and the multiplicative stochastic noises. The missing measurements are governed by a sequence of random variables obeying the Bernoulli distribution. For the purpose of energy saving, an event-triggered communication scheme is used for DSMNNs to determine whether the measurement output is transmitted to the estimator or not. The problem addressed is to design an event-triggered estimator such that the dynamics of the estimation error is exponentially mean-square stable and the prespecified disturbance rejection attenuation level is also guaranteed. By utilizing a Lyapunov-Krasovskii functional and stochastic analysis techniques, sufficient conditions are derived to guarantee the existence of the desired estimator, and then, the estimator gains are characterized in terms of the solution to certain matrix inequalities. Finally, a numerical example is used to demonstrate the usefulness of the proposed event-triggered state estimation scheme.

Closeness-Centrality-Based Synchronization Criteria for Complex Dynamical Networks With Interval Time-Varying Coupling Delays

This paper investigates synchronization in complex dynamical networks (CDNs) with interval time-varying delays. The CDNs are representative of systems composed of a large number of interconnected dynamical units, and for the purpose of the mathematical analysis, the leading work is to model them as graphs whose nodes represent the dynamical units. At this time, we take note of the importance of each node in networks. One way, in this paper, is that the closeness-centrality mentioned in the field of social science is grafted onto the CDNs. By constructing a suitable Lyapunov-Krasovskii functional, and utilizing some mathematical techniques, the sufficient and closeness-centrality-based conditions for synchronization stability of the networks are established in terms of linear matrix inequalities. Ultimately, the use of the closeness-centrality can be weighted with regard to not only the interconnection relation among the nodes, which was utilized in the existing works but also more information about nodes. Here, the centrality will be added as the concerned information. Moreover, to avoid the computational burden causing the nonconvex term including the square of the time-varying delay, how to deal with it is applied by estimating it to the convex term including time-varying delay. Finally, two illustrative examples are given to show the advantage of the closeness-centrality in point of the robustness on time-delay.

State Estimation for Discrete Time-Delayed Genetic Regulatory Networks With Stochastic Noises Under the Round-Robin Protocols

This paper investigates the problem of state estimation for discrete time-delayed genetic regulatory networks with stochastic process noises and bounded exogenous disturbances under the Round-Robin (RR) protocols. The network measurement outputs obtained by two groups of sensors are transmitted to two remote sub-estimators via two independent communication channels, respectively. To lighten the communication loads of the networks and reduce the occurrence rate of data collisions, two RR protocols are utilized to orchestrate the transmission orders of sensor nodes in two groups, respectively. The error dynamics of the state estimation is governed by a switched system with periodic switching parameters. By constructing a transmission-order-dependent Lyapunov-like functional and utilizing the up-to-date discrete Wirtinger-based inequality together with the reciprocally convex approach, sufficient conditions are established to guarantee the exponentially ultimate boundedness of the estimation error dynamics in mean square with a prescribed upper bound on the decay rate. An asymptotic upper bound of the outputs of the estimation errors in mean square is derived and the estimator parameters are then obtained by minimizing such an upper bound subject to linear matrix inequality constraints. The repressilator model is utilized to illustrate the effectiveness of the designed estimator.

Finite-Horizon $H_\infty $ Consensus for Multiagent Systems With Redundant Channels via An Observer-Type Event-Triggered Scheme

This paper is concerned with the finite-horizon consensus problem for a class of discrete time-varying multiagent systems with external disturbances and missing measurements. To improve the communication reliability, redundant channels are introduced and the corresponding protocol is constructed for the information transmission over redundant channels. An event-triggered scheme is adopted to determine whether the information of agents should be transmitted to their neighbors. Subsequently, an observer-type event-triggered control protocol is proposed based on the latest received neighbors' information. The purpose of the addressed problem is to design a time-varying controller based on the observed information to achieve the consensus performance in a finite horizon. By utilizing a constrained recursive Riccati difference equation approach, some sufficient conditions are obtained to guarantee the consensus performance, and the controller parameters are also designed. Finally, a numerical example is provided to demonstrate the desired reliability of redundant channels and the effectiveness of the event-triggered control protocol.

Variance-Constrained State Estimation for Nonlinearly Coupled Complex Networks

This paper studies the state estimation problem for nonlinearly coupled complex networks. A variance-constrained state estimator is developed by using the structure of the extended Kalman filter, where the gain matrix is determined by optimizing an upper bound matrix for the estimation error covariance despite the linearization errors and coupling terms. Compared with the existing estimators for linearly coupled complex networks, a distinct feature of the proposed estimator is that the gain matrix can be derived separately for each node by solving two Riccati-like difference equations. By using the stochastic analysis techniques, sufficient conditions are established which guarantees the state estimation error is bounded in mean square. A numerical example is provided to show the effectiveness and applicability of the proposed estimator.