Observer-Based Bounded H∞ Control for Shift-Varying Linear Repetitive Processes With Constrained Bit Rates Over a Finite Horizon

This technical correspondence examines the issue of observer-based bounded $H_{\infty }$ control for a kind of shift-varying linear repetitive process (LRP) over networks with constrained bit rates in the finite horizon. Unlike the previous researches that address (or avoid) the problem of limited network resources by designing different scheduling protocols, this study focuses on further reducing and optimizing the bandwidth utilization by introducing a bit rate constraint model. Thus, an encoding-decoding mechanism under the constrained bit rates is proposed based on the quantization method. In order to analyze the $H_{\infty }$ performance of the LRP and design an appropriate controller, the LRP is transformed into a shift-varying two-dimensional (2-D) Fornasini-Marchesini model. Sufficient conditions in recursive linear matrix inequalities are proposed to ensure that the extended system achieves a bounded $H_{\infty }$ performance over a finite horizon within the 2-D framework. Furthermore, a component-based strategy for allocating the bit rates is provided to expand the quantization region under the constraint of bit rates. Finally, the effectiveness of the proposed method is verified by a simulation example.

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.

A refined adaptive event-based resilient filtering for complex networks over switching topology

The problem of the resilient filtering for a class of discrete-time complex networks over switching topology is investigated. Taking into account the limitation of channel bandwidth, a refined adaptive event-triggered scheme is derived, whose threshold is determined by the change rate of measurement. The large change rate of measurement results in a smaller threshold, which means that more data packets will be transmitted to guarantee the performance of filtering, and the smaller one leads to a bigger threshold to save the network energy. Under the adaptive event-triggered scheme, considering the switching topology and uncertain inner coupling, a resilient filtering with a variable filtering gain is proposed. Additionally, the minimal upper bound of the covariance of estimation error is developed and the sufficient conditions are also given to obtain the exponentially bounded in mean square of the estimation error system. Finally, a simulation is presented to certify the effectiveness of the derived resilient filtering.

H∞ state estimation of continuous-time neural networks with uncertainties

[Formula: see text] state estimation is addressed for continuous-time neural networks in the paper. The norm-bounded uncertainties are considered in communication neural networks. For the considered neural networks with uncertainties, a reduced-order [Formula: see text] state estimator is designed, which makes that the error dynamics is exponentially stable and has weighted [Formula: see text] performance index by Lyapunov function method. Moreover, it is also given the devised method of the reduced-order [Formula: see text] state estimator. Then, considering that sampling the output y(t) of the neural network at every moment will result in waste of excess resources, the event-triggered sampling strategy is used to solve the oversampling problem. In addition, a devised method is also given for the event-triggered reduced-order [Formula: see text] state estimator. Finally, by the well-known Tunnel Diode Circuit example, it shows that a lower order state estimator can be designed under the premise of maintaining the same weighted [Formula: see text] performance index, and using the event-triggered sampling method can reduce the computational and time costs and save communication resources.

Bounded Antisynchronization of Multiple Neural Networks via Multilevel Hybrid Control

The bounded antisynchronization (AS) problem of multiple discrete-time neural networks (NNs) based on the fuzzy model is studied, in consideration of the differences in quantity and communication among different NN groups, the variabilities of dynamics, and communication topological affected by environments. To reduce the energy consumption of communication, a cluster pinning communication mechanism is proposed, and an impulsive observer is designed to estimate the state of target NN. Then, a multilevel hybrid controller based on the impulsive observer is built including the AS controller and the bounded synchronization (BS) controller. Sufficient conditions for bounded AS are obtained by analyzing the stability of the BS augmented error (BSAE) and the AS augmented error (ASAE) based on the fuzzy-based Lyapunov functional (FBLF). Finally, a numerical example and an application example are given to verify the validity of the obtained results.

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.

Bounded synchronization for uncertain master-slave neural networks: An adaptive impulsive control approach

This paper investigates the bounded synchronization of the discrete-time master-slave neural networks (MSNNs) with uncertainty. To deal with the unknown parameter in the MSNNs, a parameter adaptive law combined with the impulsive mechanism is proposed to improve the estimation efficiency. Meanwhile, the impulsive method also is applied to the controller design for saving the energy. In addition, a novel time-varying Lyapunov functional candidate is employed to depict the impulsive dynamical characteristic of the MSNNs, wherein a convex function related to the impulsive interval is used to obtain a sufficient condition for bounded synchronization of the MSNNs. Based on the above condition, the controller gain is calculated utilizing an unitary matrix. An algorithm is proposed to reduce the boundary of the synchronization error by optimizing its parameters. Finally, a numerical example is provided to illustrate the correctness and the superiority of the developed results.

Pinning Impulsive Synchronization of Stochastic Delayed Neural Networks via Uniformly Stable Function

This article investigates the synchronization of stochastic delayed neural networks under pinning impulsive control, where a small fraction of nodes are selected as the pinned nodes at each impulsive moment. By proposing a uniformly stable function as a new tool, some novel mean square decay results are presented to analyze the error system obtained from the leader and the considered neural networks. For the divergent error system without impulsive effects, the impulsive gains of pinning impulsive controller can admit destabilizing impulse and the number of destabilizing impulse may be infinite. However, if the error system without impulsive effects is convergent, to achieve the synchronization of the stochastic neural networks, the growth exponent of the product of impulsive gains can not exceed some positive constant. It is shown that the obtained results increase the flexibility of the impulsive gains compared with the existing results. Finally, a numerical example is given to illustrate the practicality of synchronization criteria.

H∞ filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H_∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system's matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H_∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H_∞ filtering approach are demonstrated via a practical example.

Synchronization of discrete fractional-order complex networks with and without unknown topology

This paper studies the outer synchronization problem of discrete fractional complex networks (DFCNs) with and without the presence of unknown topology. A discrete complex network with a fractional difference is first established and analyzed. By constructing a suitable Lyapunov function and utilizing properties of the fractional difference, outer synchronization criteria for the DFCNs with and without unknown topology are established based on linear matrix inequalities. Meanwhile, the unknown parameters in the topology structure of the network can be identified by adaptive update laws. In the end, two numerical examples are given to exemplify the validity and applicability of the obtained results.

H∞ synchronization of delayed neural networks via event-triggered dynamic output control

This paper investigates H_∞ exponential synchronization (ES) of neural networks (NNs) with delay by designing an event-triggered dynamic output feedback controller (ETDOFC). The ETDOFC is flexible in practice since it is applicable to both full order and reduced order dynamic output techniques. Moreover, the event generator reduces the computational burden for the zero-order-hold (ZOH) operator and does not induce sampling delay as many existing event generators do. To obtain less conservative results, the delay-partitioning method is utilized in the Lyapunov-Krasovskii functional (LKF). Synchronization criteria formulated by linear matrix inequalities (LMIs) are established. A simple algorithm is provided to design the control gains of the ETDOFC, which overcomes the difficulty induced by different dimensions of the system parameters. One numerical example is provided to demonstrate the merits of the theoretical analysis.

Mixed H2/H∞ State Estimation for Discrete-Time Switched Complex Networks With Random Coupling Strengths Through Redundant Channels

This article investigates the mixed H₂/H_∞ state estimation problem for a class of discrete-time switched complex networks with random coupling strengths through redundant communication channels. A sequence of random variables satisfying certain probability distributions is employed to describe the stochasticity of the coupling strengths. A redundant-channel-based data transmission mechanism is adopted to enhance the reliability of the transmission channel from the sensor to the estimator. The purpose of the addressed problem is to design a state estimator for each node, such that the error dynamics achieves both the stochastic stability (with probability 1) and the prespecified mixed H₂/H_∞ performance requirement. By using the switched system theory, an extensive stochastic analysis is carried out to derive the sufficient conditions ensuring the stochastic stability as well as the mixed H₂/H_∞ performance index. The desired state estimator is also parameterized by resorting to the solutions to certain convex optimization problems. A numerical example is provided to illustrate the validity of the proposed estimation scheme.

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.

Variance-Constrained Recursive State Estimation for Time-Varying Complex Networks With Quantized Measurements and Uncertain Inner Coupling

In this paper, a new recursive state estimation problem is discussed for a class of discrete time-varying stochastic complex networks with uncertain inner coupling and signal quantization under the error-variance constraints. The coupling strengths are allowed to be varying within certain intervals, and the measurement signals are subject to the quantization effects before being transmitted to the remote estimator. The focus of the conducted topic is on the design of a variance-constrained state estimation algorithm with the aim to ensure a locally minimized upper bound on the estimation error covariance at every sampling instant. Furthermore, the boundedness of the resulting estimation error is analyzed, and a sufficient criterion is established to ensure the desired exponential boundedness of the state estimation error in the mean square sense. Finally, some simulations are proposed with comparisons to illustrate the validity of the newly developed variance-constrained estimation method.

Finite-Time Synchronization and H∞ Synchronization of Multiweighted Complex Networks With Adaptive State Couplings

In this paper, two kinds of multiweighted and adaptive state coupled complex networks (CNs) with or without coupling delays are presented. First, we develop the appropriate state feedback controller and adaptive law for the sake of guaranteeing that the proposed network models without coupling delays can be finite-timely synchronized and H_∞ synchronized. Furthermore, for the multiweighted CNs with coupling delays and adaptive state couplings, some finite-time synchronization and H_∞ synchronization criteria are presented by choosing the appropriate adaptive law and controllers. Eventually, we give two numerical simulations to verify the validity of the theoretical results.

Finite-Horizon l2-l∞ Synchronization for Time-Varying Markovian Jump Neural Networks Under Mixed-Type Attacks: Observer-Based Case

This paper studies the synchronization issue of time-varying Markovian jump neural networks (NNs). The denial-of-service (DoS) attack is considered in the communication channel connecting master NNs and slave NNs. An observer is designed based on the measurements of master NNs transmitted over this unreliable channel to estimate their states. The deception attack is used to destroy the controller by changing the sign of the control signal. Then, the mixed-type attacks are expressed uniformly, and a synchronization error system is established using this function. A finite-horizon l₂-l_∞ performance is proposed, and sufficient conditions are derived to ensure that the synchronization error system satisfies this performance. The controllers are then obtained by a recursive linear matrix inequality algorithm. At last, a simulation result to show the feasibility of the developed results is given.

An Event-Triggered Pinning Control Approach to Synchronization of Discrete-Time Stochastic Complex Dynamical Networks

This paper is concerned with the synchronization analysis and control problems for a class of nonlinear discrete-time stochastic complex dynamical networks (CDNs) consisting of identical nodes. The discrete-time stochastic dynamical networks under consideration are quite general that account for asymmetric coupling configuration, nonlinear inner coupling structures as well as nonidentical exogenous disturbances. By resorting to both the error bound and the synchronization probability, a notion of quasi-synchronization in probability is first introduced to assess the synchronization performance of the addressed CDNs. An event-triggered pinning feedback control strategy is adopted to control a small fraction of the network nodes with hope to reduce the frequency of updating and communication in the control process while preserving the desired dynamical behaviors of the controlled networks. By using the Lyapunov function method and the stochastic analysis techniques, a general framework is established within which the problems of dynamics analysis and controller synthesis are solved for the closed-loop stochastic dynamical networks. Two numerical examples and their simulations are presented to illustrate the effectiveness and the usefulness of our theoretical results.

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.

Asynchronous State Estimation for Discrete-Time Switched Complex Networks With Communication Constraints

This paper is concerned with the asynchronous state estimation for a class of discrete-time switched complex networks with communication constraints. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the topology/coupling information. Also, the event-based communication, signal quantization, and the random packet dropout problems are studied due to the limited communication resource. With the help of switched system theory and by resorting to some stochastic system analysis method, a sufficient condition is proposed to guarantee the exponential stability of estimation error system in the mean-square sense and a prescribed performance level is also ensured. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem. Finally, the effectiveness of the proposed design approach is demonstrated by a simulation example.

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.

State Estimation for General Complex Dynamical Networks with Incompletely Measured Information

Estimating uncertain state variables of a general complex dynamical network with randomly incomplete measurements of transmitted output variables is investigated in this paper. The incomplete measurements, occurring randomly through the transmission of output variables, always cause the failure of the state estimation process. Different from the existing methods, we propose a novel method to handle the incomplete measurements, which can perform well to balance the excessively deviated estimators under the influence of incomplete measurements. In particular, the proposed method has no special limitation on the node dynamics compared with many existing methods. By employing the Lyapunov stability theory along with the stochastic analysis method, sufficient criteria are deduced rigorously to ensure obtaining the proper estimator gains with known model parameters. Illustrative simulation for the complex dynamical network composed of chaotic nodes are given to show the validity and efficiency of the proposed method.

Event-Based $H_\infty $ State Estimation for Time-Varying Stochastic Dynamical Networks With State- and Disturbance-Dependent Noises

In this paper, the event-based finite-horizon H_∞ state estimation problem is investigated for a class of discrete time-varying stochastic dynamical networks with state- and disturbance-dependent noises [also called (x,v) -dependent noises]. An event-triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator, where the signal is transmitted only when certain conditions are satisfied. The purpose of the problem addressed is to design a time-varying state estimator in order to estimate the network states through available output measurements. By employing the completing-the-square technique and the stochastic analysis approach, sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed H_∞ performance constraint over a finite horizon. The desired estimator parameters can be designed via solving coupled backward recursive Riccati difference equations. Finally, a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme.

State Estimation for Discrete-Time Dynamical Networks With Time-Varying Delays and Stochastic Disturbances Under the Round-Robin Protocol

This paper is concerned with the state estimation problem for a class of nonlinear dynamical networks with time-varying delays subject to the round-robin protocol. The communication between the state estimator and the nodes of the dynamical networks is implemented through a shared constrained network, in which only one node is allowed to send data at each time instant. The round-robin protocol is utilized to orchestrate the transmission order of nodes. By using a switch-based approach, the dynamics of the estimation error is modeled by a periodic parameter-switching system with time-varying delays. The purpose of the problem addressed is to design an estimator, such that the estimation error is exponentially ultimately bounded with a certain asymptotic upper bound in mean square subject to the process noise and exogenous disturbance. Furthermore, such a bound is subsequently minimized by the designed estimator parameters. A novel Lyapunov-like functional is employed to deal with the dynamics analysis issue of the estimation error. Sufficient conditions are established to guarantee the ultimate boundedness of the estimation error in mean square by applying the stochastic analysis approach. Then, the desired estimator gains are characterized by solving a convex problem. Finally, a numerical example is given to illustrate the effectiveness of the estimator design scheme.

Non-fragile mixed H∞ and passive synchronization of Markov jump neural networks with mixed time-varying delays and randomly occurring controller gain fluctuation

This paper studies the non-fragile mixed H∞ and passive synchronization problem for Markov jump neural networks. The randomly occurring controller gain fluctuation phenomenon is investigated for non-fragile strategy. Moreover, the mixed time-varying delays composed of discrete and distributed delays are considered. By employing stochastic stability theory, synchronization criteria are developed for the Markov jump neural networks. On the basis of the derived criteria, the non-fragile synchronization controller is designed. Finally, an illustrative example is presented to demonstrate the validity of the control approach.

Finite-Time State Estimation for Coupled Markovian Neural Networks With Sensor Nonlinearities

This paper investigates the issue of finite-time state estimation for coupled Markovian neural networks subject to sensor nonlinearities, where the Markov chain with partially unknown transition probabilities is considered. A Luenberger-type state estimator is proposed based on incomplete measurements, and the estimation error system is derived by using the Kronecker product. By using the Lyapunov method, sufficient conditions are established, which guarantee that the estimation error system is stochastically finite-time bounded and stochastically finite-time stable, respectively. Then, the estimator gains are obtained via solving a set of coupled linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed new design method.

Asynchronous Dissipative State Estimation for Stochastic Complex Networks With Quantized Jumping Coupling and Uncertain Measurements

This paper addresses the problem of state estimation for a class of discrete-time stochastic complex networks with a constrained and randomly varying coupling and uncertain measurements. The randomly varying coupling is governed by a Markov chain, and the capacity constraint is handled by introducing a logarithmic quantizer. The uncertainty of measurements is modeled by a multiplicative noise. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the coupling information, and an augmented estimation error system is obtained using the Kronecker product. Sufficient conditions are established, which guarantee that the estimation error system is stochastically stable and achieves the strict (Q, S, R)-γ-dissipativity. Then, the estimator gains are derived using the linear matrix inequality method. Finally, a numerical example is provided to illustrate the effectiveness of the proposed new design techniques.

Graph Theory-Based Pinning Synchronization of Stochastic Complex Dynamical Networks

This paper is concerned with the adaptive pinning synchronization problem of stochastic complex dynamical networks (CDNs). Based on algebraic graph theory and Lyapunov theory, pinning controller design conditions are derived, and the rigorous convergence analysis of synchronization errors in the probability sense is also conducted. Compared with the existing results, the topology structures of stochastic CDN are allowed to be unknown due to the use of graph theory. In particular, it is shown that the selection of nodes for pinning depends on the unknown lower bounds of coupling strengths. Finally, an example on a Chua's circuit network is given to validate the effectiveness of the theoretical results.

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

In this paper, the state estimation problem is investigated for a class of discrete-time complex networks subject to nonlinearities, mixed delays, and stochastic noises. A set of event-based state estimators is constructed so as to reduce unnecessary data transmissions in the communication channel. Compared with the traditional state estimator whose measurement signal is received under a periodic clock-driven rule, the event-based estimator only updates the measurement information from the sensors when the prespecified "event" is violated. Attention is focused on the analysis and design problem of the event-based estimators for the addressed discrete-time complex networks such that the estimation error is exponentially bounded in mean square. A combination of the stochastic analysis approach and Lyapunov theory is employed to obtain sufficient conditions for ensuring the existence of the desired estimators and the upper bound of the estimation error is also derived. By using the convex optimization technique, the gain parameters of the desired estimators are provided in an explicit form. Finally, a simulation example is used to demonstrate the effectiveness of the proposed estimation strategy.

Synchronization Control of Neural Networks With State-Dependent Coefficient Matrices

This brief is concerned with synchronization control of a class of neural networks with state-dependent coefficient matrices. Being different from the existing drive-response neural networks in the literature, a novel model of drive-response neural networks is established. The concepts of uniformly ultimately bounded (UUB) synchronization and convex hull Lyapunov function are introduced. Then, by using the convex hull Lyapunov function approach, the UUB synchronization design of the drive-response neural networks is proposed, and a delay-independent control law guaranteeing the bounded synchronization of the neural networks is constructed. All present conditions are formulated in terms of bilinear matrix inequalities. By comparison, it is shown that the neural networks obtained in this brief are less conservative than those ones in the literature, and the bounded synchronization is suitable for the novel drive-response neural networks. Finally, an illustrative example is given to verify the validity of the obtained results.