Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays

Composite intelligent learning-based tracking control for discrete-time repetitive process

In this work, a new composite iterative learning control (ILC) algorithm for the tracking issue of a class of discrete-time systems that operate repetitively over a finite time duration is developed. Particularly, the proposed intelligent learning process consists of two phases to achieve an enhanced tracking performance: the gain-adaptive iterative learning control (GAILC) phase and the sliding mode iterative learning control (SMILC) phase, respectively. Moreover, the switching of the two phases is determined by the tracking error. For GAILC phase, a prediction of tracking error based adaptive gain sequence is adopted to achieve a fast convergence in tracking error. For SMILC phase, an appropriate sliding surface function in the iteration domain is established, and then a novel SMILC law with a fractional power term is presented to achieve a high tracking precision. Finally, comparative simulations including a DC motor example are provided to validate the effectiveness and advantage of the proposed ILC strategy.

Self-Organizing Robust Fuzzy Neural Network for Nonlinear System Modeling

Fuzzy neural network (FNN) is a structured learning technique that has been successfully adopted in nonlinear system modeling. However, since there exist uncertain external disturbances arising from mismatched model errors, sensor noises, or unknown environments, FNN generally fails to achieve the desirable performance of modeling results. To overcome this problem, a self-organization robust FNN (SOR-FNN) is developed in this article. First, an information integration mechanism (IIM), consisting of partition information and individual information, is introduced to dynamically adjust the structure of SOR-FNN. The proposed mechanism can make itself adapt to uncertain environments. Second, a dynamic learning algorithm based on the -divergence loss function ( -DLA) is designed to update the parameters of SOR-FNN. Then, this learning algorithm is able to reduce the sensibility of disturbances and improve the robustness of Third, the convergence of SOR-FNN is given by the Lyapunov theorem. Then, the theoretical analysis can ensure the successful application of SOR-FNN. Finally, the proposed SOR-FNN is tested on several benchmark datasets and a practical application to validate its merits. The experimental results indicate that the proposed SOR-FNN can obtain superior performance in terms of model accuracy and robustness.

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.

Dual periodic event-triggered control for multi-agent systems with input saturation

This paper is concerned with the periodic event-triggered consensus of multi-agent systems subject to input saturation. Due to the nonlinearity caused by the input saturation constraint, the accuracy of the event-triggered mechanism to screen data will be reduced. To deal with this problem, a novel dual periodic event-triggered mechanism is first proposed, in which a saturation-assisted periodic event-trigger and a complemental periodic event-trigger work synergistically to screen data more efficiently under the input saturation constraint. In addition, considering the various disturbances in the environment, a more general mixed H_∞ and passive performance is introduced to describe the disturbance attenuation level. Based on the Lyapunov-Krasovskii functional, some less conservative consensus criteria are obtained for the multi-agent systems. In addition, under different input saturation constraints, the relationship between the disturbance attenuation level and the data transmission rate is explored. After that, a particle swarm optimization algorithm is a first attempt to estimate and enlarge the region of asymptotic consensus. Finally, an example is given to verify the effectiveness and superiority of our proposed method.

Global Stability of Bidirectional Associative Memory Neural Networks With Multiple Time-Varying Delays

This article investigates the global stability of bidirectional associative memory neural networks with discrete and distributed time-varying delays (DBAMNNs). By employing the comparison strategy and inequality techniques, global asymptotic stability (GAS) and global exponential stability (GES) of the underlying DBAMNNs are of concern in terms of p -norm ( p ≥ 2 ). Meanwhile, GES of the addressed DBAMNNs is also analyzed in terms of 1-norm. When distributed time delay is neglected, the GES of the corresponding bidirectional associative memory neural networks is presented as an M -matrix, which includes certain existing outcomes as special cases. Two examples are finally provided to substantiate the validity of theories.

Finite-Time Extended Dissipative Filtering for Singular T-S Fuzzy Systems With Nonhomogeneous Markov Jumps

This article investigates the finite-time extended dissipative filtering for singular T-S fuzzy Markov jump systems with time-varying transition probabilities (TPs). The time-varying TPs are considered to reside in a polytope. By resorting to a generalized performance index, the H_∞ , L₂-L_∞ , passive, and dissipative performance can be solved in a unified framework. Combining the free-weighting method and the proposed recursive method, a sufficient condition on singular stochastic extended dissipative finite-time boundedness (SSEDFTB) for a fuzzy filtering error system is obtained. By proposing a decoupling principle called double variables-based decoupling principle (DVDP) and a variable substitution principle (VSP), a novel condition on the existence of the fuzzy filter is presented in terms of linear matrix inequalities (LMIs). Compared with the existing works, the assumption on state variables and the constraints of slack matrices are overcome, which leads to more practical and less conservative results. A practical example is provided to demonstrate the effectiveness of the design methods.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov-Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

Design and Implementation of Deep Neural Network-Based Control for Automatic Parking Maneuver Process

This article focuses on the design, test, and validation of a deep neural network (DNN)-based control scheme capable of predicting optimal motion commands for autonomous ground vehicles (AGVs) during the parking maneuver process. The proposed design utilizes a multilayer structure. In the first layer, a desensitized trajectory optimization method is iteratively performed to establish a set of time-optimal parking trajectories with the consideration of noise-perturbed initial configurations. Subsequently, by using the preplanned optimal parking trajectory data set, several DNNs are trained in order to learn the functional relationship between the system state-control actions in the second layer. To obtain further improvements regarding the DNN performances, a simple yet effective data aggregation approach is designed and applied. These trained DNNs are then utilized as the motion controllers to generate feedback actions in real time. Numerical results were executed to demonstrate the effectiveness and the real-time applicability of using the proposed control scheme to plan and steer the AGV parking maneuver. Experimental results were also provided to justify the algorithm performance in real-world implementations.

Event-Triggered H∞ Control for T-S Fuzzy Systems via New Asynchronous Premise Reconstruction Approach

This article studies the problem of H_∞ controller design for discrete-time T-S fuzzy systems under an event-triggered (ET) communication mechanism. By proposing a new asynchronous premise reconstruction approach, new types of ET fuzzy controllers are designed to overcome the challenges caused by the mismatch of premise variables, in which the gains of the designed controllers are automatically updated at different triggering instants according to an online algorithm. By constructing discontinuous Lyapunov functions, it is proved that the proposed ET controllers guarantee the stability and H_∞ performance of the closed-loop systems. Two examples are provided to verify the validity of the proposed design method.

Finite-time H∞ sliding mode control of uncertain T-S fuzzy system with time-varying delay based on observer

In this paper, a class of observer-based sliding mode controller is designed, and the finite-time H∞ control problem of uncertain T-S fuzzy systems with time-varying is studied. Firstly, an integral-type sliding surface function with time-delay is devised based on the state estimator, and sufficient criteria of finite-time bounded and finite-time H∞ bounded can be obtained for the T-S systems. Moreover, the proposed sliding mode control law is integrated to ensure the dynamics of controlled system into the sliding surface in a finite-time interval. Then, according to the linear matrix inequalities (LMIs), the desired gain matrices of fuzzy sliding mode controller and state estimator are derived. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.

Dynamic event-based state estimation for delayed artificial neural networks with multiplicative noises: A gain-scheduled approach

This study is concerned with the state estimation issue for a kind of delayed artificial neural networks with multiplicative noises. The occurrence of the time delay is in a random way that is modeled by a Bernoulli distributed stochastic variable whose occurrence probability is time-varying and confined within a given interval. A gain-scheduled approach is proposed for the estimator design to accommodate the time-varying nature of the occurrence probability. For the sake of utilizing the communication resource as efficiently as possible, a dynamic event triggering mechanism is put forward to orchestrate the data delivery from the sensor to the estimator. Sufficient conditions are established to ensure that, in the simultaneous presence of the external noises, the randomly occurring time delays with time-varying occurrence probability as well as the dynamic event triggering communication protocol, the estimation error is exponentially ultimately bounded in the mean square. Moreover, the estimator gain matrices are explicitly calculated in terms of the solution to certain easy-to-solve matrix inequalities. Simulation examples are provided to show the validity of the proposed state estimation method.

Hidden Markov Model-Based Nonfragile State Estimation of Switched Neural Network With Probabilistic Quantized Outputs

This paper focuses on the state estimator design problem for a switched neural network (SNN) with probabilistic quantized outputs, where the switching process is governed by a sojourn probability. It is assumed that both packet dropouts and signal quantization exist in communication channels. Asynchronous estimator and quantification function are described by two different hidden Markov model between the SNNs and its estimator. To deal with the small uncertain of estimators in a random way, a probabilistic nonfragile state estimator is introduced, where uncertain information is described by the interval type of gain variation. A sufficient condition on mean square stable of the estimation error system is obtained and then the desired estimator is designed. Finally, a simulation result is provided to verify the effectiveness of the proposed design method.

Event-Based Dissipative Analysis for Discrete Time-Delay Singular Jump Neural Networks

This paper investigates the event-triggered dissipative filtering issue for discrete-time singular neural networks with time-varying delays and Markovian jump parameters. Via event-triggered communication technique, a singular jump neural network (SJNN) model of network-induced delays is first given, and sufficient criteria are then provided to guarantee that the resulting augmented SJNN is stochastically admissible and strictly stochastically dissipative (SASSD) with respect to (X_ι,Y_ι,Z_ι,δ) by using slack matrix scheme. Furthermore, employing filter equivalent technique, codesigned filter gains, and event-triggered matrices are derived to make sure that the augmented SJNN model is SASSD with respect to (X_ι,Y_ι,Z_ι,δ) . An example is also given to illustrate the effectiveness of the proposed method.

Asynchronous and Resilient Filtering for Markovian Jump Neural Networks Subject to Extended Dissipativity

The problem of asynchronous and resilient filtering for discrete-time Markov jump neural networks subject to extended dissipativity is investigated in this paper. The modes of the designed resilient filter are assumed to run asynchronously with the modes of original Markov jump neural networks, which accord well with practical applications and are described through a hidden Markov model. Due to the fluctuation of the filter parameters, a resilient filter taking into account parameter uncertainty is adopted. Being different from the norm-bound type of uncertainty which has been studied in a considerable number of the existing literatures, the interval type of uncertainty is introduced so as to describe uncertain phenomenon more accurately. By means of convex optimal method, the gains of filter are derived to guarantee the stochastic stability and extended dissipativity of the filtering error system under the wave of the filter parameters. Considering the limited computing power of MATLAB solver, a relatively simple simulation is exploited to verify the effectiveness and merits of the theoretical findings where the relationships among optimal performance index, uncertain parameter σ , and asynchronous rate are revealed.

Finite-Time H∞ Filtering for Nonlinear Singular Systems With Nonhomogeneous Markov Jumps

This paper addresses the finite-time H_∞ filtering for a class of nonlinear singular nonhomogeneous Markov jump systems by T-S fuzzy approximation approach, where the transition probabilities (TPs) are time-varying and unknown. First, by considering a stochastic Lyapunov functional and rendering the time-varying TPs inside a polytope, a sufficient condition on singular stochastic H_∞ finite-time boundedness (SS H_∞ FTB) for the filtering error systems is given. Then, by using the matrix inequality decoupling technique, a novel linear matrix inequality (LMI) condition on the existence of the finite-time H_∞ fuzzy filter is presented. The fuzzy filter is developed in terms of LMIs ensuring the filtering error system is SS H_∞ FTB. Compared with the previous ones, the proposed design method in this paper has more freedom, leading to less conservative results. A tunnel diode circuit is provided to illustrate the effectiveness and advantage of the design approach proposed in this paper.

Double-Loop Stability for High Frequency Networked Control Systems Subject to Actuator Saturation

This paper generalizes stability for a high frequency networked control system (NCS) subject to actuator saturation via integral quadratic constraints. A delta operator system with a high frequency constraint is used to model the high frequency NCS. Double-loop stability is treated via outer-loop and interloop feedback configurations for the high frequency NCS. Stability criteria are derived with the high frequency constraint and actuator saturation by a generalized Kalman-Yakubovich-Popov lemma. Numerical results are provided to demonstrate the effectiveness of the proposed techniques in this paper.

Generalized State Estimation for Markovian Coupled Networks Under Round-Robin Protocol and Redundant Channels

In this paper, the problem of generalized state estimation for an array of Markovian coupled networks under the round-Robin protocol (RRP) and redundant channels is investigated by using an extended dissipative property. The randomly varying coupling of the networks under consideration is governed by a Markov chain. With the aid of using the RRP, the transmission order of nodes is availably orchestrated. In this case, the probability of occurrence data collisions through a shared constrained network may be reduced. The redundant channels are also used in the signal transmission to deal with the frangibility of networks caused by a single channel in the networks. The network induced phenomena, that is, randomly occurring packet dropouts and randomly occurring quantization are fully considered. The main purpose of the research is to find a desired estimator design approach such that the extended (Ω₁,Ω₂,Ω₃) - γ -stochastic dissipativity property of the estimation error system is guaranteed. In terms of the Lyapunov-Krasovskii methodology, the Kronecker product and an improved matrix decoupling approach, sufficient conditions for such an addressed problem are established by means of handling some convex optimization problems. Finally, the serviceability of the proposed method is explained by providing an illustrated example.

Exponential Stabilization of Fuzzy Memristive Neural Networks With Hybrid Unbounded Time-Varying Delays

This paper is concerned with exponential stabilization for a class of Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with unbounded discrete and distributed time-varying delays. Under the framework of Filippov solutions, algebraic criteria are established to guarantee exponential stabilization of the addressed FMNNs with hybrid unbounded time delays via designing a fuzzy state feedback controller by exploiting inequality techniques, calculus theorems, and theories of fuzzy sets. The obtained results in this paper enhance and generalize some existing ones. Meanwhile, a general theoretical framework is proposed to investigate the dynamical behaviors of various neural networks with mixed infinite time delays. Finally, two simulation examples are performed to illustrate the validity of the derived outcomes.

Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities

In this paper, we study the problem of finite-time stability and passivity criteria for discrete-time neural networks (DNNs) with variable delays. The main objective is how to effectively evaluate the finite-time passivity conditions for NNs. To achieve this, some new weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of a novel Lyapunov-Krasovskii functional, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed results.

Nonfragile State Estimation of Quantized Complex Networks With Switching Topologies

This paper considers the nonfragile $H_\infty $ estimation problem for a class of complex networks with switching topologies and quantization effects. The network architecture is assumed to be dynamic and evolves with time according to a random process subject to a sojourn probability. The coupled signal is to be quantized before transmission due to power and bandwidth constraints, and the quantization errors are transformed into sector-bounded uncertainties. The concept of nonfragility is introduced by inserting randomly occurred uncertainties into the estimator parameters to cope with the unavoidable small gain variations emerging from the implementations of estimators. Both the quantizers and the estimators have several operation modes depending on the switching signal of the underlying network structure. A sufficient condition is provided via a linear matrix inequality approach to ensure the estimation error dynamic to be stochastically stable in the absence of external disturbances, and the $H_\infty $ performance with a prescribed index is also satisfied. Finally, a numerical example is presented to clarify the validity of the proposed method.

Stability Analysis of Quaternion-Valued Neural Networks: Decomposition and Direct Approaches

In this paper, we investigate the global stability of quaternion-valued neural networks (QVNNs) with time-varying delays. On one hand, in order to avoid the noncommutativity of quaternion multiplication, the QVNN is decomposed into four real-valued systems based on Hamilton rules: $ij=-ji=k,~jk=-kj=i$ , $ki=-ik=j$ , $i^{2}=j^{2}=k^{2}=ijk=-1$ . With the Lyapunov function method, some criteria are, respectively, presented to ensure the global $\mu $ -stability and power stability of the delayed QVNN. On the other hand, by considering the noncommutativity of quaternion multiplication and time-varying delays, the QVNN is investigated directly by the techniques of the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) where quaternion self-conjugate matrices and quaternion positive definite matrices are used. Some new sufficient conditions in the form of quaternion-valued LMI are, respectively, established for the global $\mu $ -stability and exponential stability of the considered QVNN. Besides, some assumptions are presented for the two different methods, which can help to choose quaternion-valued activation functions. Finally, two numerical examples are given to show the feasibility and the effectiveness of the main results.

Learning With Coefficient-Based Regularized Regression on Markov Resampling

Big data research has become a globally hot topic in recent years. One of the core problems in big data learning is how to extract effective information from the huge data. In this paper, we propose a Markov resampling algorithm to draw useful samples for handling coefficient-based regularized regression (CBRR) problem. The proposed Markov resampling algorithm is a selective sampling method, which can automatically select uniformly ergodic Markov chain (u.e.M.c.) samples according to transition probabilities. Based on u.e.M.c. samples, we analyze the theoretical performance of CBRR algorithm and generalize the existing results on independent and identically distributed observations. To be specific, when the kernel is infinitely differentiable, the learning rate depending on the sample size $m$ can be arbitrarily close to $\mathcal {O}(m^{-1})$ under a mild regularity condition on the regression function. The good generalization ability of the proposed method is validated by experiments on simulated and real data sets.

Variance-Constrained State Estimation for Complex Networks With Randomly Varying Topologies

This paper investigates the variance-constrained state estimation problem for a class of nonlinear time-varying complex networks with randomly varying topologies, stochastic inner coupling, and measurement quantization. A Kronecker delta function and Markovian jumping parameters are utilized to describe the random changes of network topologies. A Gaussian random variable is introduced to model the stochastic disturbances in the inner coupling of complex networks. As a kind of incomplete measurements, measurement quantization is taken into consideration so as to account for the signal distortion phenomenon in the transmission process. Stochastic nonlinearities with known statistical characteristics are utilized to describe the stochastic evolution of the complex networks. We aim to design a finite-horizon estimator, such that in the simultaneous presence of quantized measurements and stochastic inner coupling, the prescribed variance constraints on the estimation error and the desired performance requirements are guaranteed over a finite horizon. Sufficient conditions are established by means of a series of recursive linear matrix inequalities, and subsequently, the estimator gain parameters are derived. A simulation example is presented to illustrate the effectiveness and applicability of the proposed estimator design algorithm.

Stability Analysis of Genetic Regulatory Networks With Switching Parameters and Time Delays

This paper is concerned with the exponential stability analysis of genetic regulatory networks (GRNs) with switching parameters and time delays. In this paper, a new integral inequality and an improved reciprocally convex combination inequality are considered. By using the average dwell time approach together with a novel Lyapunov-Krasovskii functional, we derived some conditions to ensure the switched GRNs with switching parameters and time delays are exponentially stable. Finally, we give two numerical examples to clarify that our derived results are effective.

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay

Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

Stability Analysis and Application for Delayed Neural Networks Driven by Fractional Brownian Noise

This paper deals with two types of the stability problem for the delayed neural networks driven by fractional Brownian noise (FBN). The existence and the uniqueness of the solution to the main system with respect to FBN are proved via fixed point theory. Based on Hilbert-Schmidt operator theory and analytic semigroup principle, the mild solution of the stochastic neural networks is obtained. By applying the stochastic analytic technique and some well-known inequalities, the asymptotic stability criteria and the exponential stability condition are established. Both numerical example and practical application for synchronization control of multiagent system are provided to illustrate the effectiveness and potential of the proposed techniques.

Mixed H∞ and passive filtering for switched Takagi-Sugeno fuzzy systems with average dwell time

This paper investigates the mixed H_∞ and passive filtering problem for switched Takagi-Sugeno (T-S) fuzzy systems with average dwell time (ADT) in both continuous-time and discrete-time contexts. To deal with this problem, a new performance index is proposed for switched systems. This new performance index can be viewed as the mixed weighted H_∞ and passivity performance index. Based on this new performance index, the weighted H_∞ filtering problem and the passive filtering problem for switched T-S fuzzy systems can be solved in a unified framework. Combining the multiple Lyapunov functions approach with a matrix decoupling technique, new sufficient conditions for the existence of mixed weighted H_∞ and passive filters are obtained for switched T-S fuzzy systems. All these conditions are expressed in terms of linear matrix inequalities (LMIs). The desired filters can be constructed by solving these LMIs. Finally, numerical examples and practical examples are provided.

Global Asymptotic Stability and Stabilization of Neural Networks With General Noise

Neural networks (NNs) in the stochastic environment were widely modeled as stochastic differential equations, which were driven by white noise, such as Brown or Wiener process in the existing papers. However, they are not necessarily the best models to describe dynamic characters of NNs disturbed by nonwhite noise in some specific situations. In this paper, general noise disturbance, which may be nonwhite, is introduced to NNs. Since NNs with nonwhite noise cannot be described by Itô integral equation, a novel modeling method of stochastic NNs is utilized. By a framework in light of random field approach and Lyapunov theory, the global asymptotic stability and stabilization in probability or in the mean square of NNs with general noise are analyzed, respectively. Criteria for the concerned systems based on linear matrix inequality are proposed. Some examples are given to illustrate the effectiveness of the obtained results.

Ontology-Based Method for Fault Diagnosis of Loaders

This paper proposes an ontology-based fault diagnosis method which overcomes the difficulty of understanding complex fault diagnosis knowledge of loaders and offers a universal approach for fault diagnosis of all loaders. This method contains the following components: (1) An ontology-based fault diagnosis model is proposed to achieve the integrating, sharing and reusing of fault diagnosis knowledge for loaders; (2) combined with ontology, CBR (case-based reasoning) is introduced to realize effective and accurate fault diagnoses following four steps (feature selection, case-retrieval, case-matching and case-updating); and (3) in order to cover the shortages of the CBR method due to the lack of concerned cases, ontology based RBR (rule-based reasoning) is put forward through building SWRL (Semantic Web Rule Language) rules. An application program is also developed to implement the above methods to assist in finding the fault causes, fault locations and maintenance measures of loaders. In addition, the program is validated through analyzing a case study.

Event-Triggered Fault Estimation for Stochastic Systems over Multi-Hop Relay Networks with Randomly Occurring Sensor Nonlinearities and Packet Dropouts

Wireless sensors have many new applications where remote estimation is essential. Considering that a remote estimator is located far away from the process and the wireless transmission distance of sensor nodes is limited, sensor nodes always forward data packets to the remote estimator through a series of relays over a multi-hop link. In this paper, we consider a network with sensor nodes and relay nodes where the relay nodes can forward the estimated values to the remote estimator. An event-triggered remote estimator of state and fault with the corresponding data-forwarding scheme is investigated for stochastic systems subject to both randomly occurring nonlinearity and randomly occurring packet dropouts governed by Bernoulli-distributed sequences to achieve a trade-off between estimation accuracy and energy consumption. Recursive Riccati-like matrix equations are established to calculate the estimator gain to minimize an upper bound of the estimator error covariance. Subsequently, a sufficient condition and data-forwarding scheme are presented under which the error covariance is mean-square bounded in the multi-hop links with random packet dropouts. Furthermore, implementation issues of the theoretical results are discussed where a new data-forwarding communication protocol is designed. Finally, the effectiveness of the proposed algorithms and communication protocol are extensively evaluated using an experimental platform that was established for performance evaluation with a sensor and two relay nodes.