This paper investigates the problem ofl2-l∞proportional-integral state estimation for stochastic nonlinear systems over decode-and-forward relay networks subject to packet losses. The system model is formulated to capture the effects of stochastic nonlinearities and state saturations, thereby reflecting practical engineering conditions. To alleviate transmission distance limitations, a decode-and-forward relay is introduced into the wireless channel to support communication from the sensor to the remote estimator, which enhances the reliability of long-distance data transmission. The objective is to design a proportional-integral state estimator that guarantees a prescribed finite-horizonl2-l∞performance level for the estimation error dynamics, despite the presence of stochastic nonlinearities, state saturations, packet losses, and decoding errors. A sufficient condition for the existence of such an estimator is established, and the corresponding estimator gains are obtained by solving a set of matrix equalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed state estimation scheme.

In this article, the social power evolution problem is investigated for a social network with a centralized media and multiple DeGroot individuals, where the centralized media impacts the evolution of individuals’ opinions through the centralization parameter at the broadcast moment, while the network topology among the individuals is influenced by the relative interaction matrix. Then, the convergence of the corresponding opinion dynamics on the time scale is derived by discussing three distinct initial social powers. By integrating the reflected appraisal mechanism, a social power evolution model with the centralized media is established, which is essentially a nonlinear mapping. Based on the Jacobian matrix of this nonlinear mapping, it is proved that both the social powers of the centralized media and DeGroot individuals can converge provided that the centralization parameter exceeds a certain threshold; furthermore, a lower bound for the centralized media’s final social power is estimated, which helps to demonstrate that the centralized media possesses the greatest social power within the whole network. Additionally, concerning individuals’ final social powers, all individuals are first divided into three categories, and a sufficient condition is presented to ensure that the balanced individual has the greatest social power except for the centralized media. Finally, the obtained results are illustrated by a numerical example.

In this article, the evolution of social power is studied within a unified framework comprising two classes of individuals: oblivious individuals and stubborn individuals, whose opinion dynamics are described by the DeGroot averaging model and the Friedkin-Johnsen model, respectively. A proper subset of the simplex is identified to ensure the well-posedness of social power, and it is demonstrated that the corresponding opinion dynamics is convergent for each issue by restricting the initial social power to this proper subset. Through the reflected appraisal mechanism, a nonlinear mapping governing the social power evolution together with its invariant set is derived, and some sufficient conditions with linear time complexity for the convergence of social power are established by proving that this nonlinear mapping is contractive on the invariant set. Furthermore, for the final social power, it is found that both autocratic and democratic social power cannot be achieved during the evolution, and the average social power of oblivious individuals is larger than that of stubborn individuals, indicating that the network topology has a greater impact on social power than individual stubbornness. In addition, it is observed that the final social power ranking of oblivious individuals is consistent with their centrality ranking, and a rigorous lower bound on the final social power is derived for each stubborn individual. Finally, a numerical example is provided to demonstrate the correctness of the theoretical analysis.

For the problem of tracking maritime dim targets, the sequential Monte–Carlo multi-Bernoulli track-before-detect (SMC-MB-TBD) method is popular. However, this method may face low tracking accuracy and tracking loss due to particle impoverishment and velocity uncertainty. In this study, a novel filter called position scaling and velocity correction multi-Bernoulli (PSVC-MB) is proposed to deal with this problem. First, particle position scaling is used to replace resampling in the SMC-MB-TBD method to deal with the lack of particle diversity. Second, when the target is stably tracked, the target velocity is extracted from the multi-frame information and used for re-estimation. Pseudo point measurements are calculated from the weighted average of all locations near the particle position, and the particle velocity will be continuously corrected with the pseudo point measurements. Simulation results verify the effectiveness of the proposed method at different low signal-to-clutter ratios (SCRs).

To address the problem of underwater multi-sensor multi-target passive tracking in clutter, a distributed kernel mean embedding-based Gaussian belief propagation (DKME-GaBP) algorithm is proposed. First, a joint posterior probability density function (PDF) is established and factorized, and it is represented by the corresponding factor graph. Then, the GaBP algorithm is executed on this factor graph to reduce the computational complexity of data association. The factor graph of the GaBP consists of inner and outer loops. The inner loop is responsible for local track estimation and data association. The outer loop fuses information from different sensors. For the inner loop, the kernel mean embedding (KME) with a Gaussian kernel is designed to transform the strong nonlinear problem of local estimation into a linear problem in a high-dimensional reproducing kernel Hilbert space (RKHS). For the outer loop, a multi-sensor distributed fusion method based on KME is proposed to improve fusion accuracy by accounting for the distance among different PDFs in RKHS. The effectiveness and robustness of the DKME-GaBP are validated in the simulations.

This paper proposes a novel dual-mode dynamic event-triggered control framework designed specifically for nonlinear cyber-physical systems (CPS) subject to constraints and bounded disturbances. The framework addresses critical challenges in balancing system performance, computation efficiency, and communication overhead. To achieve this, two distinct control modes are developed based on the system state’s location relative to the terminal set. When the system state lies outside the terminal set, Mode 1 is activated. This mode implements an event-triggered model predictive control approach, combining a dynamic threshold with a PID-based triggering mechanism. These features notably reduce the frequency of triggering events while also lowering computation and communication costs. In contrast, Mode 2 becomes active when the system state lies within the terminal set. This mode employs an event-triggered feedback control approach aimed at further reducing communication costs while maintaining control efficiency. In addition, rigorous theoretical analysis is conducted to establish the recursive feasibility, stability, and exclusion of Zeno behavior within the proposed framework. Finally, numerical simulations are performed to validate the superiority of the proposed method.

Energy harvesting wireless sensor networks (EHWSNs) face significant challenges, including unpredictable energy availability, communication disruptions, and nonlinear state estimation. This work addresses the distributed moving horizon estimation problem over EHWSNs. First, we establish models for the energy harvesting process, dynamic evolution of energy level, and information transmission, complemented by a priority-based energy allocation mechanism to manage inter-sensor communication. Unlike existing approaches that typically assume known statistical properties of the energy harvesting process, this work treats communication intermittency, resulting from the unpredictability of energy availability and energy allocation strategy, as a switching network topology, thereby eliminating the need to calculate the probability of successful information transmission. Subsequently, based on switched system theory that contains both stable and unstable subsystems, a novel distributed moving horizon estimator (DMHE) framework suitable for nonlinear systems under bounded disturbances is designed to achieve accurate state estimation. A case study on vehicle localization demonstrates that the proposed method maintains high estimation accuracy even in complex scenarios with disconnected network topologies; specifically, if each sensor’s energy harvesting rate is 0.8, the root mean square error (RMSE) is less than 0.06.

In this article, the set-membership state estimation problem is investigated for a class of nonlinear complex networks under the FlexRay protocols (FRPs). In order to address practical engineering requirements, the multirate sampling is taken into account which allows for different sampling periods of the system state and the measurement. On the other hand, the FRP is deployed in the communication network from sensors to estimators in order to alleviate the communication burden. The underlying nonlinearity studied in this article is of a general nature, and an approach based on neural networks is employed to handle the nonlinearity. By utilizing the convex optimization technique, sufficient conditions are established in order to restrain the estimation errors within certain ellipsoidal constraints. Then, the estimator gains and the tuning scalars of the neural network are derived by solving several optimization problems. Finally, a practical simulation is conducted to verify the validity of the developed set-membership estimation scheme.

This article deals with the distributed proportional–integral state estimation problem for nonlinear systems over sensor networks (SNs), where a number of spatially distributed sensor nodes are utilized to collect the system information. The signal transmissions among different sensor nodes are realized via their individual channels subject to energy-constrained Denial-of-Service (EC-DoS) cyber-attacks launched by the adversaries whose aim is to block the nodewise communications. Such EC-DoS attacks are characterized by a sequence of attack starting time-instants and a sequence of attack durations. Based on the measurement outputs of each node, a novel distributed fuzzy proportional–integral estimator is proposed that reflects the topological information of the SNs. The estimation error dynamics is shown to be regulated by a switching system under certain assumptions on the frequency and the duration of the EC-DoS attacks. Then, by resorting to the average dwell-time method, a unified framework is established to analyze the dynamical behaviors of the resultant estimation error system, and sufficient conditions are obtained to guarantee the stability as well as the weighted$H_{\infty}$performance of the estimation error dynamics. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme.

This article is concerned with the state estimation problem for a class of complex networks (CNs) with uncertain inner couplings and packet losses over communication networks. The inner couplings are allowed to be uncertain and varying in a specific interval. The amplify-and-forward (AaF) relay protocols are introduced to improve the communication quality and enhance the propagation distance. The Bernoulli random variables are used to characterize the randomly occurring packet losses encountered in communication channels. The focus of this article is on the design of a state estimator for each node of CNs such that a prescribed performance constraint is satisfied for the dynamical error system over a finite horizon. A sufficient condition is first provided to verify the existence of the desired state estimator, and the estimator gain is then determined by solving two coupled backward Riccati difference equations (RDEs). Subsequently, a recursive state estimation algorithm is put forward that is suitable for online computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed estimation method.

This article is concerned with a new partial-neurons-based proportional-integral observer (PIO) design problem for a class of artificial neural networks (ANNs) subject to bounded disturbances. For the purpose of improving the reliability of the data transmission, the multiple description encoding mechanisms are exploited to encode the measurement data into two identically important descriptions, and the encoded data are then transmitted to the decoders via two individual communication channels susceptible to packet dropouts, where Bernoulli-distributed stochastic variables are utilized to characterize the random occurrence of the packet dropouts. An explicit relationship is discovered that quantifies the influences of the packet dropouts on the decoding accuracy, and a sufficient condition is provided to assess the boundedness of the estimation error dynamics. Furthermore, the desired PIO parameters are calculated by solving two optimization problems based on two metrics (i.e., the smallest ultimate bound and the fastest decay rate) characterizing the estimation performance. Finally, the applicability and advantage of the proposed PIO design strategy are verified by means of an illustrative example.

This article is concerned with the finite-horizon$H_{\infty}$state estimation problem for a specific class of nonlinear complex dynamical networks (CDNs) which are subject to random couplings and packet dropouts. The random coupling strengths among network nodes are characterized by a set of random variables with known statistical information. Three sequences of Bernoulli distributed random variables are utilized to model the packet dropouts over different communication channels. A decode-and-forward relay-based strategy is implemented to enhance the quality of communication by controlling the signal transmission in each sensor-to-estimator channel. The primary goal of this investigation is to create an appropriate state estimator for each node of the CDN, enabling the fulfillment of a specific$H_{\infty}$performance requirement for the estimation error dynamics over a finite horizon. Through the use of stochastic analysis techniques and matrix operations, a preliminary sufficient condition is given to meet the finite-horizon$H_{\infty}$performance requirement. The expected estimator gains are subsequently determined, which are defined in terms of the solutions to a series of recursive matrix inequalities. The effectiveness of the proposed relay-based estimation scheme is ultimately demonstrated through a numerical example.

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.

In this article, the simultaneous state and fault estimation problem is investigated for a class of nonlinear 2-D shift-varying systems, where the sensors and the estimator are connected via a communication network of limited bandwidth. With the purpose of relieving the communication burden and enhancing the transmission security, a new encoding-decoding mechanism is put forward so as to encode the transmitted data with a finite number of bits. The aim of the addressed problem is to develop a neural-network (NN)-based set-membership estimator for jointly estimating the system states and the faults, where the estimation errors are guaranteed to reside within an optimized ellipsoidal set. With the aid of the mathematical induction technique and certain convex optimization approaches, sufficient conditions are derived for the existence of the desired set-membership estimator, and the estimator gains and the NN tuning scalars are then presented in terms of the solutions to a set of optimization problems subject to ellipsoidal constraints. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed estimator design method.

In this article, the nonfragile filtering issue is addressed for complex networks (CNs) with switching topologies, sensor saturations, and dynamic event-triggered communication protocol (DECP). Random variables obeying the Bernoulli distribution are utilized in characterizing the phenomena of switching topologies and stochastic gain variations. By introducing an auxiliary offset variable in the event-triggered condition, the DECP is adopted to reduce transmission frequency. The goal of this article is to develop a nonfragile filter framework for the considered CNs such that the upper bounds on the filtering error covariances are ensured. By the virtue of mathematical induction, gain parameters are explicitly derived via minimizing such upper bounds. Moreover, a new method of analyzing the boundedness of a given positive-definite matrix is presented to overcome the challenges resulting from the coupled interconnected nodes, and sufficient conditions are established to guarantee the mean-square boundedness of filtering errors. Finally, simulations are given to prove the usefulness of our developed filtering algorithm.

This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques.

This article is concerned with the problem of finite-horizon H∞state estimation for time-varying coupled stochastic networks through the round-robin scheduling protocol. The inner coupling strengths of the considered coupled networks are governed by a random sequence with known expectations and variances. For the sake of mitigating the occurrence probability of the network-induced phenomena, the communication network is equipped with the round-robin protocol that schedules the signal transmissions of the sensors' measurement outputs. By using some dedicated approximation techniques, an uncertain auxiliary system with stochastic parameters is established where the multiplicative noises enter the coefficient matrix of the augmented disturbances. With the established auxiliary system, the desired finite-horizon H∞state estimator is acquired by solving coupled backward Riccati equations, and the corresponding recursive estimator design algorithm is presented that is suitable for online application. The effectiveness of the proposed estimator design method is validated via a numerical example.

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.

This paper is concerned with the problem of distributed H∞ filtering for switched stochastic time-delay systems with fading measurements over sensor networks. The underlying target plants are subject to fading measurements where the fading rates are described by continuous-time random variables with known statistical properties dependent on the system modes. The adjacency matrices characterizing the topology of the sensor networks are also allowed to be mode-dependent. Based on the multiple Lyapunov functional approach and average dwell-time concept, the distributed H∞filter is designed by means of the convex optimization scheme. A dedicated technique is developed via a simple algebraic equality in order to avoid solving a transcendental equation used in the existing results. With the designed filter, the error dynamics of the state estimation is guaranteed to have the mean-square exponential stability with a prescribed H∞disturbance attenuation level. Finally, a numerical example is used to demonstrate the effectiveness of the method.

This paper proposes a novel event-triggered (ET) adaptive neural control scheme for a class of discrete-time nonlinear systems in a strict-feedback form. In the proposed scheme, the ideal control input is derived in a recursive design process, which relies on system states only and is unrelated to virtual control laws. In this case, the high-order neural networks (NNs) are used to approximate the ideal control input (but not the virtual control laws), and then the corresponding adaptive neural controller is developed under the ET mechanism. A modified NN weight updating law, nonperiodically tuned at triggering instants, is designed to guarantee the uniformly ultimate boundedness (UUB) of NN weight estimates for all sampling times. In virtue of the bounded NN weight estimates and a dead-zone operator, the ET condition together with an adaptive ET threshold coefficient is constructed to guarantee the UUB of the closed-loop networked control system through the Lyapunov stability theory, thereby largely easing the network communication load. The proposed ET condition is easy to implement because of the avoidance of: 1) the use of the intermediate ET conditions in the backstepping procedure; 2) the computation of virtual control laws; and 3) the redundant triggering of events when the system states converge to a desired region. The validity of the presented scheme is demonstrated by simulation results.

This paper focuses on the observer-based output-feedback control (OBOFC) problem for a class of discrete-time strict-feedback nonlinear systems (DTSFNSs) with both multiplicative process noises and additive measurement noises. A state observer is first designed to estimate immeasurable system states, and then a novel observer-based backstepping control framework is proposed for DTSFNSs with known model information. To be specific, virtual control laws and the actual control law are derived using a variable substitution method that gets rid of the repeated accumulation of measurement noises in the recursive process. Furthermore, for technical derivation, the multiplicative noise is successively bounded by state estimation errors and controlled errors. Stability conditions are obtained to guarantee the exponential mean-square boundedness of the closed-loop system. Moreover, the nonlinear modeling uncertainties are taken into account to better reflect engineering practices. In virtue of the universal approximation property of fuzzy-logic systems, a fuzzy observer and the corresponding fuzzy output-feedback controller are simultaneously constructed to derive the stability criteria by using novel weight updated laws. Simulation studies are performed to test the validity of the proposed OBOFC scheme.

In this article, the design problem of the proportional-integral observer (PIO) is investigated for a class of discrete-time multidelayed recurrent neural networks (RNNs). In the addressed RNN model, the delays occurring in the information interconnections are allowed to be different, and the phenomenon of sensor saturation is taken into consideration in the measurement model. A novel dynamic event-triggered protocol is employed in the data transmission from sensors to the observer with hope to improve the efficiency of resource utilization, where the threshold parameters are adaptive to the dynamical environment. By virtue of the Lyapunov-like approach, a general framework is established for examining the boundedness of the estimation errors in mean-square sense, and the ultimate bound of the error dynamics is also acquired. Subsequently, the explicit expression of the desired PIO is parameterized by using the matrix inequality techniques. Finally, a simulation example is utilized to verify the effectiveness and superiority of the proposed PIO design scheme.

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.

This paper investigates the event-triggered (ET) tracking control problem for a class of discrete-time strict-feedback nonlinear systems subject to both stochastic noises and limited controller-to-actuator communication capacities. The ET mechanism with fixed triggering threshold is designed to decide whether the current control signal should be transmitted to the actuator. A systematic framework is developed to construct a novel adaptive neural controller by directly applying the backstepping procedure to the underlying system. The proposed framework overcomes the noncausality problem, avoids the possible controller-related singularity problem, and gets rid of the neural approximation of the virtual control laws. Under the ET mechanism, the corresponding ET-based actuator is put forward by introducing an ET threshold compensation operator. Such a compensation operator (with an adjustable design parameter) is subtly designed based on a hyperbolic tangent function and a sign function. The threshold compensation error is analytically characterized in terms of a time-varying parameter, and the error bound is shown to be relatively small that is dependent on the adjustable design parameter. Compared with the traditional ET-based actuator without the compensation operator, the proposed ET-based actuator exhibits several distinguished features including: 1) improvement of the tracking accuracy (especially at the triggering instants); 2) further mitigation of the communication load; and 3) enlargement of the allowable range of the ET threshold. These features are illustrated by numerical and practical examples.

This paper addresses the control problem of the switched system with bounded actuators and average dwell-time. We present the switching rules for the designed controllers based on two kinds of parametric algebraic Riccati equation. The exponential stability of the switched system under the average-dwell time is ensured by the designed controllers and the switching rules. The dynamic performance of the control system is enhanced greatly by the proposed method. The simulation results illustrate the effectiveness and the usefulness of the obtained theoretical results.

This paper is concerned with the problem of mean-square exponential stability of uncertain neural networks with time-varying delay and stochastic perturbation. Both linear and nonlinear stochastic perturbations are considered. The main features of this paper are twofold: 1) Based on generalized Finsler lemma, some improved delay-dependent stability criteria are established, which are more efficient than the existing ones in terms of less conservatism and lower computational complexity; and 2) when the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions, the restrictive condition P < δI (or the similar ones) in the existing results can be relaxed under some assumptions. The usefulness of the proposed method is demonstrated by illustrative examples.

The problem of state estimation for Markovian jumping Hopfield neural networks (MJHNNs) with delays is addressed in this paper. It is assumed that sector- bounded conditions are obeyed by the neuron activation function and perturbed function of the measurement equation. An LMI (linear matrix inequality) based state estimator and a stability criterion for delay MJHNNs are developed. It is shown that the designed estimator ensures the mean-square exponential stability of the resulting error system. Moreover, the delay-dependent sufficient conditions are derived in a simple and effective manner. Numerical results are presented which show that the proposed method is very promising for state estimation of Hopfield neural networks.

This brief focuses on the robust mean-square exponential stability and L(2) performance analysis for a class of uncertain time-delay neural networks perturbed by both additive and multiplicative stochastic noises. New mean-square exponential stability and L(2) performance criteria are developed based on the delay partition Lyapunov-Krasovskii functional method and generalized Finsler lemma which is applicable to stochastic systems. The analytical results are established without involving any model transformation, estimation for cross terms, additional free-weighting matrices, or tuning parameters. Numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones.