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

Maximum Correntropy Filtering for Complex Networks With Uncertain Dynamical Bias: Enabling Componentwise Event-Triggered Transmission

This article is concerned with the maximum correntropy filtering (MCF) problem for a class of nonlinear complex networks subject to non-Gaussian noises and uncertain dynamical bias. With aim to utilize the constrained network bandwidth and energy resources in an efficient way, a componentwise dynamic event-triggered transmission (DETT) protocol is adopted to ensure that each sensor component independently determines the time instant for transmitting data according to the individual triggering condition. The principal purpose of the addressed problem is to put forward a dynamic event-triggered recursive filtering scheme under the maximum correntropy criterion, such that the effects of the non-Gaussian noises can be attenuated. In doing so, a novel correntropy-based performance index (CBPI) is first proposed to reflect the impacts from the componentwise DETT mechanism, the system nonlinearity, and the uncertain dynamical bias. The CBPI is parameterized by deriving upper bounds on the one-step prediction error covariance and the equivalent noise covariance. Subsequently, the filter gain matrix is designed by means of maximizing the proposed CBPI. Finally, an illustrative example is provided to substantiate the feasibility and effectiveness of the developed MCF scheme.

EEGProgress: A fast and lightweight progressive convolution architecture for EEG classification

Because of the intricate topological structure and connection of the human brain, extracting deep spatial features from electroencephalograph (EEG) signals is a challenging and time-consuming task. The extraction of topological spatial information plays a crucial role in EEG classification, and the architecture of the spatial convolution greatly affects the performance and complexity of convolutional neural network (CNN) based EEG classification models. In this study, a progressive convolution CNN architecture named EEGProgress is proposed, aiming to efficiently extract the topological spatial information of EEG signals from multi-scale levels (electrode, brain region, hemisphere, global) with superior speed. To achieve this, the raw EEG data is permuted using the empirical topological permutation rule, integrating the EEG data with numerous topological properties. Subsequently, the spatial features are extracted by a progressive feature extractor including prior, electrode, region, and hemisphere convolution blocks, progressively extracting the deep spatial features with reduced parameters and speed. Finally, the comparison and ablation experiments under both cross-subject and within-subject scenarios are conducted on a public dataset to verify the performance of the proposed EEGProgress and the effectiveness of the topological permutation. The results demonstrate the superior feature extraction ability of the proposed EEGProgress, with an average increase of 4.02% compared to other CNN-based EEG classification models under both cross-subject and within-subject scenarios. Furthermore, with the obtained average testing time, FLOPs, and parameters, the proposed EEGProgress outperforms other comparison models in terms of model complexity.

Outlier-Resistant State Estimation for Singularly Perturbed Complex Networks With Nonhomogeneous Sojourn Probabilities

This study investigates an outlier-resistant state estimation problem for singularly perturbed complex networks (SPCNs) with sojourn probabilities and randomly occurring coupling strengths. Aiming at better describing the dynamic behavior of the network topology for SPCNs, a novel switching law associated with the time-varying sojourn probabilities is developed, and the variation of sojourn probabilities is arranged by a high-level deterministic switching signal. Meanwhile, a sequence of mode-dependent variables is employed to describe the randomly occurring coupling strength. Subsequently, to alleviate the side effects from possible measurement outliers, a dynamic saturation function-based state estimator is designed, whose saturation level is adaptively varying based on previous estimation errors. In virtue of Lyapunov theory and mode-dependent average dwell-time strategy, it can be verified that the resulting dynamics is stochastic H∞ finite-time bounded. To this end, a simulation example is presented to show the validity of the proposed estimator design method.

Distributed Extended State Estimation for Complex Networks With Nonlinear Uncertainty

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

Cluster Synchronization Control for Discrete-Time Complex Dynamical Networks: When Data Transmission Meets Constrained Bit Rate

In this article, the cluster synchronization control problem is studied for discrete-time complex dynamical networks when the data transmission is subject to constrained bit rate. A bit-rate model is presented to quantify the limited network bandwidth, and the effects from the constrained bit rate onto the control performance of the cluster synchronization are evaluated. A sufficient condition is first proposed to guarantee the ultimate boundedness of the error dynamics of the cluster synchronization, and then, a bit-rate condition is established to reveal the fundamental relationship between the bit rate and the certain performance index of the cluster synchronization. Subsequently, two optimization problems are formulated to design the desired synchronization controllers with aim to achieve two distinct synchronization performance indices. The codesign issue for the bit-rate allocation protocol and the controller gains is further discussed to reduce the conservatism by locally minimizing a certain asymptotic upper bound of the synchronization error dynamics. Finally, three illustrative simulation examples are utilized to validate the feasibility and effectiveness of the developed synchronization control scheme.

Neural-Network-Based Set-Membership Fault Estimation for 2-D Systems Under Encoding-Decoding Mechanism

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.

Energy-to-Peak State Estimation With Intermittent Measurement Outliers: The Single-Output Case

This article is concerned with the energy-to-peak state estimation problem for a class of linear discrete-time systems with energy-bounded noises and intermittent measurement outliers (IMOs). In order to capture the intermittent nature, two sequences of step functions are introduced to model the occurrence of the IMOs. Furthermore, two special indices (i.e., minimum and maximum interval lengths) are adopted to describe the "occurrence frequency" of IMOs. Different from the considered energy-bounded noises, the outliers are assumed to have their magnitudes larger than certain thresholds. In order to achieve a satisfactory performance constraint on the energy-to-peak state estimation under the addressed kind of measurement outliers, a novel parameter-dependent (PD) state estimation strategy is developed to guarantee that the measurements contaminated by outliers would be removed in the estimation process. The proposed PD state estimation method is essentially a two-step process, where the first step is to examine the appearing and disappearing moments for each IMO by using a dedicatedly constructed outlier detection scheme, and the second step is to implement the state estimation task according to the outlier detection results. Sufficient conditions are obtained to ensure the existence of the desired estimator, and the gain matrix of the desired estimator is then derived by solving a constrained optimization problem. Finally, a simulation example is presented to illustrate the effectiveness of our developed PD state estimation strategy.

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

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

Simultaneous State and Unknown Input Estimation for Complex Networks With Redundant Channels Under Dynamic Event-Triggered Mechanisms

This article addresses the simultaneous state and unknown input estimation problem for a class of discrete time-varying complex networks (CNs) under redundant channels and dynamic event-triggered mechanisms (ETMs). The redundant channels, modeled by an array of mutually independent Bernoulli distributed stochastic variables, are exploited to enhance transmission reliability. For energy-saving purposes, a dynamic event-triggered transmission scheme is enforced to ensure that every sensor node sends its measurement to the corresponding estimator only when a certain condition holds. The primary objective of the investigation carried out is to construct a recursive estimator for both the state and the unknown input such that certain upper bounds on the estimation error covariances are first guaranteed and then minimized at each time instant in the presence of dynamic event-triggered strategies and redundant channels. By solving two series of recursive difference equations, the desired estimator gains are computed. Finally, an illustrative example is presented to show the usefulness of the developed estimator design method.

H∞ Proportional-Integral State Estimation for T-S Fuzzy Systems Over Randomly Delayed Redundant Channels With Partly Known Probabilities

In this article, we consider the H_∞ proportional-integral (PI) state estimation (SE) problem for discrete-time T-S fuzzy systems subject to transmission delays, external disturbances, and redundant channels. Multiple redundant communication channels are utilized between the sensors and the remote estimator to enhance the reliability of data transmissions. In order to characterize the transmission delays in network-based communication, a family of random variables with partly known probabilities, which are independent and identically distributed, is adopted to describe the random behavior of the transmission delays with the redundant channels. The objective of this work is to put forward a PI state estimator such that the dynamics of the estimation error is exponentially mean-square stable and satisfies the prescribed H_∞ performance index of the disturbance attenuation/rejection. By employing the stochastic analysis approach, the error dynamics of the SE under the proposed state estimator is analyzed and sufficient conditions are obtained to ensure the existence of the required PI state estimator. Furthermore, the desired estimator parameters are derived by solving a nonlinear optimization problem. Finally, two simulation examples are exploited to demonstrate the validity of the proposed SE scheme.

A Dynamic Event-Triggered Approach to Recursive Nonfragile Filtering for Complex Networks With Sensor Saturations and Switching Topologies

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.

H∞ Pinning Control of Complex Dynamical Networks Under Dynamic Quantization Effects: A Coupled Backward Riccati Equation Approach

In this article, a pinning control strategy is developed for the finite-horizon H_∞ synchronization problem for a kind of discrete time-varying nonlinear complex dynamical network in a digital communication circumstance. For the sake of complying with the digitized data exchange, a feedback-type dynamic quantizer is introduced to reflect the transformation from the raw signals into the discrete-valued ones. Then, a quantized pinning control scheme takes place on a small fraction of the network nodes with the hope of cutting down the control expenses while achieving the expected global synchronization objective. Subsequently, by resorting to the completing-the-square technique, a sufficient condition is established to ensure the finite-horizon H_∞ index of the synchronization error dynamics against both quantization errors and external noises. Moreover, a controller design algorithm is put forward via an auxiliary H₂ -type criterion, and the desired controller gains are acquired in terms of two coupled backward Riccati equations. Finally, the validity of the presented results is verified via a simulation example.

Multiloop Decentralized H∞ Fuzzy PID-Like Control for Discrete Time-Delayed Fuzzy Systems Under Dynamical Event-Triggered Schemes

This article is concerned with the multiloop decentralized H_∞ fuzzy proportional-integral-derivative-like (PID-like) control problem for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays under dynamical event-triggered mechanisms (ETMs). The sensors of the plant are grouped into several nodes according to their physical distribution. For resource-saving purposes, the signal transmission between each sensor node and the controller is implemented based on the dynamical ETM. Taking the node-based idea into account, a general multiloop decentralized fuzzy PID-like controller is designed with fixed integral windows to reduce the potential accumulation error. The overall decentralized fuzzy PID-like control scheme involves multiple single-loop controllers, each of which is designed to generate the local control law based on the measurements of the corresponding sensor node. These kinds of local controllers are convenient to apply in practice. Sufficient conditions are obtained under which the controlled system is exponentially stable with the prescribed H_∞ performance index. The desired controller gains are then characterized by solving an iterative optimization problem. Finally, a simulation example is presented to demonstrate the correctness and effectiveness of the proposed design procedure.

Recursive state estimation for a class of nonlinear uncertain coupled complex networks subject to random link failures and packet disorders

This paper is concerned with the recursive state estimation (RSE) problem under minimum mean-square error sense for a class of nonlinear complex networks (CNs) with uncertain inner coupling, random link failures and packet disorders. Firstly, a set of random variables obeying the Bernoulli distribution is adopted to characterize whether there are connections between different network units, i.e., there is no random link failure when the random variable is equal to 1, otherwise the random link failure occurs. In addition, the inner coupling strength is assumed to be varying within a given interval and the phenomenon of packet disorders caused by the random transmission delay (RTD) is also taken into account. In our study, the nonlinearity satisfies the continuously differentiable condition, which can be linearized by resorting to the Taylor expansion. The focus of the addressed RSE problem is on the design of an RSE approach in the mean-square error sense such that, for all uncertain inner coupling, random link failures and packet disorders, a suboptimal upper bound of the state estimation error covariance is obtained and minimized by parameterizing the state estimator gain with explicit expression form. Furthermore, a sufficient condition with respect to the uniform boundedness of state estimation error in mean-square sense is elaborated. Finally, a numerical experiment is introduced to demonstrate the validity of the presented RSE approach.

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

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

A Partial-Node-Based Approach to State Estimation for Complex Networks With Sensor Saturations Under Random Access Protocol

In this article, the robust finite-horizon state estimation problem is investigated for a class of time-varying complex networks (CNs) under the random access protocol (RAP) through available measurements from only a part of network nodes. The underlying CNs are subject to randomly occurring uncertainties, randomly occurring multiple delays, as well as sensor saturations. Several sequences of random variables are employed to characterize the random occurrences of parameter uncertainties and multiple delays. The RAP is adopted to orchestrate the data transmission at each time step based on a Markov chain. The aim of the addressed problem is to design a series of robust state estimators that make use of the available measurements from partial network nodes to estimate the network states, under the RAP and over a finite horizon, such that the estimation error dynamics achieves the prescribed H_∞ performance requirement. Sufficient conditions are provided for the existence of such time-varying partial-node-based H_∞ state estimators via stochastic analysis and matrix operations. The desired estimators are parameterized by solving certain recursive linear matrix inequalities. The effectiveness of the proposed state estimation algorithm is demonstrated via a simulation example.

Outlier-Resistant Recursive Filtering for Multisensor Multirate Networked Systems Under Weighted Try-Once-Discard Protocol

In this article, a new outlier-resistant recursive filtering problem (RF) is studied for a class of multisensor multirate networked systems under the weighted try-once-discard (WTOD) protocol. The sensors are sampled with a period that is different from the state updating period of the system. In order to lighten the communication burden and alleviate the network congestions, the WTOD protocol is implemented in the sensor-to-filter channel to schedule the order of the data transmission of the sensors. In the case of the measurement outliers, a saturation function is employed in the filter structure to constrain the innovations contaminated by the measurement outliers, thereby maintaining satisfactory filtering performance. By resorting to the solution to a matrix difference equation, an upper bound is first obtained on the covariance of the filtering error, and the gain matrix of the filter is then characterized to minimize the derived upper bound. Furthermore, the exponential boundedness of the filtering error dynamics is analyzed in the mean square sense. Finally, the usefulness of the proposed outlier-resistant RF scheme is verified by simulation examples.

Distributed Resilient Estimator Design for Positive Systems Under Topological Attacks

This article is concerned with the distributed resilient estimation of a positive system over a sensor network. First, a heterogeneous sensor interaction framework, where each sensor is capable of sharing its local information of measurement as well as state estimate with its underlying neighbors via distinct interaction topologies, is proposed to account for different sensor communication capacities. During the information exchanges among the sensors, topological attacks are suitably modeled in such a way to incorporate the random and intermittent disruption of the heterogeneous sensor interaction topologies. Second, two sets of distributed resilient estimators are delicately constructed to cope with the resulting random denial of information exchanges within the specific repaired periods and compromised periods caused by the topological attacks. Third, the resilience performance analysis with a prescribed l₁ -gain attenuation level is carried out, and a linear programming approach is then developed to achieve the design of the desired distributed estimators. Finally, the effectiveness of the proposed design method is verified through a vehicle formation monitoring system.

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

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

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.

H∞ and l2-l∞ state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol

In this paper, a protocol-based finite-horizon H_∞ and l₂-l_∞ estimation approach is put forward to solve the state estimation problem for discrete-time memristive neural networks (MNNs) subject to time-varying delays and energy-bounded disturbances. The Round-Robin protocol is utilized to mitigate unnecessary network congestion occurring in the sensor-to-estimator communication channel. For the delayed MNNs, our aim is to devise an estimator that not only ensures a prescribed disturbance attenuation level over a finite time-horizon, but also keeps the peak value of the estimation error within a given range. By resorting to the Lyapunov-Krasovskii functional method, the delay-dependent criteria are formulated that guarantee the existence of the desired estimator. Subsequently, the estimator gains are obtained via figuring out a bank of convex optimization problems. The validity of our estimator is finally shown via a numerical example.

H∞ sliding mode control for Markovian jump systems with randomly occurring uncertainties and repeated scalar nonlinearities via delay-fractioning method

This paper addresses the problem of robust H_∞ sliding mode control (SMC) for discrete delayed Markovian jumping systems subject to randomly occurring uncertainties (ROUs) and repeated scalar nonlinearities (RSNs). Here, a set of mutually independent Bernoulli distributed random variables is introduced to model the phenomenon of the ROUs, where the occurrence probabilities could be uncertain. The purpose of paper is to present an H_∞ SMC strategy via the delay-fractioning approach such that, for the Markovian jumping parameters, time-varying delays, ROUs and RSNs, the mean-square stability of the resulted sliding motion with a prescribed H_∞ performance can be guaranteed. Subsequently, the robust sliding mode controller is synthesized to guarantee that the reachability condition in the discrete-time setting is ensured. Finally, the validity of proposed robust SMC strategy is verified by providing a simulation example.