Estimator Gain Matrix Research Articles

The Dynamic Event-Based Non-Fragile H∞ State Estimation for Discrete Nonlinear Systems with Dynamical Bias and Fading Measurement

The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused by unknown inputs is represented by a dynamic equation with bounded noise. Subsequently, the augmentation technique is employed and the dynamic event-triggered mechanism is introduced in the sensor-to-estimator channel to determine whether data should be transmitted or not, thereby conserving resources. Furthermore, an augmented state-dependent non-fragile state estimator is constructed considering gain perturbation of the estimator and fading measurements during network transmission. Sufficient conditions are provided based on Lyapunov stability and matrix analysis techniques to ensure exponential mean-square stability of the estimation error system while satisfying the H∞ disturbance fading level. The desired estimator gain matrix can be obtained by solving the linear matrix inequality (LMI). Finally, an example is presented to illustrate the effectiveness of the proposed method for designing estimators.

Event‐triggered nonfragile state estimation for delayed neural networks with additive and multiplicative gain variations

AbstractThis article aims to design a nonfragile state estimator for neural networks with time‐varying delay under the event‐triggered mechanism. This paper addresses the two most common issues that exist in large‐scale networks: gain variations in the estimator design and lack of network resources. Based on the nonfragile paradigm and an event‐triggered mechanism, an estimator is being developed to address this issue, considering both the additive and multiplicative structured gain variations. Through the Lyapunov–Krasovskii functional method and linear matrix inequality technique, sufficient conditions are derived to guarantee the existence of the proposed state estimator by employing the generalized free‐weighting matrix inequality and improved reciprocally convex inequality. Moreover, the obtained linear matrix inequalities provide an explicit expression of the estimator gain matrix and triggering matrix. Eventually, two numerical examples are provided to authenticate the proposed findings.

Neural-Network-Based Secure State Estimation Under Energy-Constrained Denial-of-Service Attacks: An Encoding-Decoding Scheme

This paper is concerned with the secure state estimation issue for a class of networked nonlinear systems under energy-constrained denial-of-service (EC-DoS) cyber-attacks and encoding-decoding scheme (EDS). The information transmissions between sensors and the estimator are executed via a bandwidth-limited communication network, on which the EDS is deployed to convert transmitted signals into finite-length codewords for the purpose of improving transmission efficiency. The EC-DoS attacks, whose intention is to jeopardize the network-based signal transmissions by overloading the communication resource, are assumed to occur in an intermittent way with bounded occurrence frequency/durations owing to the inherent energy constraints on the attackers. Considering the worst case of such EC-DoS attacks, a neural-network (NN)-based state estimator is constructed to generate the desired state estimates for the underlying networked nonlinear system. By employing the Lyapunov stability theory, the estimation error dynamics of the system state and the neural-network weight are jointly analyzed within a unified framework. Subsequently, sufficient conditions are obtained for the existence of the desired NN-based state estimator, and then both the desired estimator gain matrix and the NN tuning parameters are characterized. Finally, the validity of our estimation approach is confirmed by an example.

Security-Ensured State of Charge Estimation of Lithium-Ion Batteries Subject to Malicious Attacks

This paper is concerned with the secure estimation problem of the state of charge (SOC) for Lithium-ion batteries subject to deception attacks. A second-order resistor-capacitor (RC) equivalent circuit model (ECM), whose parameters are identified by means of the extended Kalman filter algorithm, is applied to characterize the static and dynamic behaviors of a Lithium-ion battery. With the aid of the polynomial-function fitting technique, the nonlinear relationship between the open circuit voltage and SOC of the ECM is established. The deception attacks launched by the malicious adversary are taken into consideration during the data transmission from the voltage/current sensor to the estimator. By employing the Lyapunov stability theory, a second-order RC-ECM-based nonlinear observer is designed in the presence of deception attacks. In addition, sufficient conditions are derived to guarantee the uniform boundedness of the estimation error and the estimator gain matrix is implicitly parameterized by solving finite linear matrix inequalities with certain constraints. Finally, the effectiveness of the proposed estimation method is verified through the experiments under the Dynamic Stress Test and Federal Urban Driving Schedule driving cycle.

Recursive state estimation for state-saturated systems with two groups of measurements: Handling delayed and degraded sensors

In this paper, the recursive fusion estimation problem is investigated for a class of state-saturated systems with two groups of sensors, one with instantaneous measurements and the other with delayed measurements. The phenomena of sensor gain degradations and sensor measurement delays are regulated by a number of mutually independent random variables that are uniformly distributed over known intervals. First, an equivalent model to the original measurement system is constructed by reorganizing the instantaneous and delayed measurements. Then, by turning to a constrained variance method, we construct an upper bound of the estimation error covariance by solving two Riccati-like recursive equations whose dimension is the same as that of the original system. Subsequently, the estimator gain matrix is computed through minimizing the constructed upper bound, and the boundedness of the acquired upper bound is also discussed. Finally, we provide a simulation example to verify the usefulness of our designed fusion estimation algorithm.

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

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

Joint state and fault estimation for nonlinear complex networks with mixed time-delays and uncertain inner coupling: non-fragile recursive method

In this paper, the non-fragile joint state and fault estimation problem is investigated for a class of nonlinear time-varying complex networks (NTVCNs) with uncertain inner coupling and mixed time-delays. Compared with the constant inner coupling strength in the existing literature, the inner coupling strength is permitted to vary within certain intervals. A new non-fragile model is adopted to describe the parameter perturbations of the estimator gain matrix which is described by zero-mean multiplicative noises. The attention of this paper is focussed on the design of a locally optimal estimation method, which can estimate both the state and the fault at the same time. Then, by reasonably designing the estimator gain matrix, the minimized upper bound of the state estimation error covariance matrix (SEECM) can be obtained. In addition, the boundedness analysis is taken into account, and a sufficient condition is provided to ensure the boundedness of the upper bound of the SEECM by using the mathematical induction. Lastly, a simulation example is provided to testify the feasibility of the joint state and fault estimation scheme.

Encoding-decoding-based finite-horizon recursive secure state estimation for dynamic coupled networks with random coupling strength☆

The recursive secure state estimator design issue is investigated in this article for a class of dynamic coupled networks (DCNs) through the encoding-decoding scheme. The random variables distributed over specified intervals are utilized to depict the stochastically varying coupling strengths. For the sake of facilitating the data transmission, saving network resources and cutting down security risks, the two-description coding scheme (TDCS) is employed in the communication channels. Based on the TDCS, the encoders are installed at two independent communication channels, and the packet loss phenomena are considered in two encoder-to-decoder channels. The random denial of service (DoS) attack is taken into account when the decoded data are transmitted to the estimator through the shared communication networks. By recursively dealing with two coupled backward Riccati difference equations (CBRDEs), the desired finite-horizon H∞ state estimator gain matrix (EGM) can be determined. Finally, a numerical example is exhibited to illustrate the efficiency of the designed finite-horizon secure state estimator.

Dynamic Event-triggered State Estimation for Nonlinear Coupled Output Complex Networks Subject to Innovation Constraints

This letter investigates the recursive state estimation (RSE) problem for a class of coupled output complex networks via the dynamic event-triggered communication mechanism (DETCM) and innovation constraints (ICs). Firstly, a DETCM is employed to regulate the transmission sequences. Then, in order to improve the reliability of network communication, a saturation function is introduced to constrain the measurement outliers. A new RSE method is provided such that, for all output coupling, DETCM and ICs, an upper bound of state estimation error covariance (SEEC) is presented in a recursive form, whose trace can be minimized via parameterizing the state estimator gain matrix (SEGM). Moreover, the theoretical analysis is given to guarantee that the error dynamic is uniformly bounded. Finally, a simulation example is illustrated to show the effectiveness of the proposed RSE method.

Adaptive event-triggered state estimation for a class of stochastic complex networks subject to coding-decoding schemes and missing measurements

This paper is concerned with the adaptive event-triggered recursive state estimation (RSE) issue for a class of nonlinear complex dynamical networks (CDNs) with random coupling parameter, missing measurements (MMs) and coding-decoding-based communication mechanism (CDBCM). First of all, a random variable uniformly distributed in a fixed interval is adopted to model the varying topologies. Then, the Bernoulli random sequence with uncertain statistical properties is considered to characterize the phenomenon of MMs subject to the uncertain occurrence probability situation. Furthermore, in order to ensure the security and reliability of the shared network channel, the adaptive event-triggered scheduling strategy (AETSS) and CDBCM are both employed to govern the data transmission thereby enhancing the communication quality. The aim of this paper is to present an RSE scheme for a class of stochastic CDNs such that for all MMs, AETSS and CDBCM, the state estimation error covariance (SEEC) is given the SEEC upper bound (SEECUB) is derived. Then, the state estimator gain matrix (SEGM) is parameterized by means of optimizing the trace of SEECUB. Moreover, the monotonicity of the trace of SEECUB with respect to the available missing probability is clarified detailed. Finally, an illustrative simulation is executed for the purpose of verifying the validity of the proposed RSE scheme.

Gain-scheduled state estimation for discrete-time complex networks under bit-rate constraints

In this paper, the gain-scheduled state estimation issue is investigated for a kind of complex networks subject to randomly occurring nonlinearities under bit-rate constraints. An array of random variables is introduced to govern the nonlinearities whose occurring probability is a time-varying but bounded value with known upper and lower bounds. A bit-rate constraint model is established and an encoding–decoding mechanism is proposed, under which an upper bound of the decoding error is acquired. The primary purpose of the issue considered in this paper is to design a gain-scheduled state estimator to obtain an estimate of the network state with an acceptable accuracy according to available output measurements. By means of the stochastic analysis and Lyapunov stability theory, a sufficient condition is provided such that the estimation error dynamics achieve the exponentially mean-square ultimate boundedness. The required estimator gain matrix is parameterized by solving a series of matrix inequalities. A numerical simulation is exploited to show the usefulness of the obtained gain-scheduled state estimator.

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.

Event-triggered recursive state estimation for dynamical networks under randomly switching topologies and multiple missing measurements

In this paper, the design problem of recursive state estimator is discussed for a class of coupled nonlinear dynamical networks with randomly switching topologies and multiple missing measurements under the event-triggered mechanism. A sequence of random variables obeying the Bernoulli distribution with certain occurrence probabilities is adopted to model the multiple missing measurements and the random change manners of the network topologies. The event-based communication protocol is introduced to adjust the transmission frequency, thereby improving the energy utilization efficiencies of the communication networks. The objective of the addressed variance-constrained estimation problem is to construct a recursive state estimator such that, in the simultaneous presence of event-based transmission strategy, randomly switching topologies as well as multiple missing measurements, a locally optimal upper bound is guaranteed on the estimation error covariance by properly determining the estimator gain, where the desired estimator gain matrix is formulated via the solutions to certain recursive matrix equations. Besides, theoretical analysis is conducted on the monotonicity regarding the missing probabilities of degraded measurements and the obtained upper bound matrix. Finally, some simulations with comparisons are carried out to demonstrate the effectiveness and feasibility of proposed event-triggered state estimation method.

A new result on L2–L∞ performance state estimation of neural networks with time-varying delay

This paper is concerned with the L2–L∞ performance state estimation problem of delayed neural networks. Firstly, the second-order Bessel–Legendre inequality based on reciprocally convex approach is proposed. Secondly, based on the improved integral inequality, a new delay-dependent condition is derived, which ensures the asymptotic stability of estimation error system with L2–L∞ performance. As a result, the estimator gain matrix and the optimal L2–L∞ performance level are obtained. Simulation results are finally shown to illustrate the effectiveness of the proposed approach.

Resilient state estimation for time‐varying uncertain dynamical networks with data packet dropouts and switching topology: an event‐triggered method

In this study, the recursive state estimation method based on the event-triggered protocol is given for time-varying uncertain complex networks with switching topology (ST), data packet dropouts (DPDs), and randomly occurring non-linearities (RONs). The event-triggered strategy is given to regulate the communications and then save the limited network resources when the measurement information is transmitted. The phenomena of RONs, ST, and DPDs are depicted by some random variables obeying the Bernoulli distribution. Besides, the estimator gain perturbations are dealt with. The major aim of this study is to present a new state estimation algorithm for addressed time-varying uncertain complex networks such that, for all STs, DPDs, and RONs, a minimal upper bound of state estimation error covariance matrix is derived by designing an optimal estimator gain matrix. Finally, a numerical simulation is presented to show the effectiveness of the provided time-varying state estimation method.

Non-fragile Suboptimal Set-membership Estimation for Delayed Memristive Neural Networks with Quantization via Maximum-error-first Protocol

This paper is concerned with the non-fragile protocol-based set-membership estimation problem for a class of discrete memristive neural networks (MNNs) with mixed time-delays, quantization and unknown but bounded noises. The nonlinear neural activation function satisfies the sector-bounded condition and the logarithmic quantization error is transformed to the norm-bounded uncertainty. In order to save the networks resources, the maximum-error-first (MEF) protocol is introduced to allocate the utilization order of the network channel. The focus is on the design of non-fragile state estimator to ensure such that, in the simultaneous presence of the mixed time-delays, quantization errors and estimator gain perturbations, real state is confined to the ellipsoid. In particular, a minimization problem is given to determine the radius of the designed ellipsoid and the estimator gain matrix by testifying the feasibility of some recursive matrix inequalities. Finally, some simulations are used to show the feasibility of the developed non-fragile suboptimal state estimation strategy.

Sampled-data state-estimation of delayed complex-valued neural networks

This paper studies the sampled-data state-estimation problem of delayed complex-valued neural networks (CVNNs). By using Lyapunov–Krasovskii functional (LKF), standard integral inequality together with the reciprocal convex approach, a delay-dependent condition is established in terms of the solution to linear matrix inequalities (LMIs) such that the consider CVNNs is asymptotically stable. As a result, an estimator gain matrix can be obtained through sampling instant. Finally, a simulation example is given to illustrate the theoretical analysis.

New result on reliable [formula omitted] performance state estimation for memory static neural networks with stochastic sampled-data communication

This work examines the H∞ performance state estimation problem for memory static neural networks (MSNNs) with reliable state feedback stochastic sampled-data control (SSDC). The purpose of presenting this study is to determine whether the H∞ performance and criteria with less conservatism for stability could be gained by SSDC for MSNNs or not. Firstly, we suppose that the sampling interval values follow Bernoulli distribution and the probability of occurrence are teadfast constant, then generalize it to a more universal form. Secondly, on basis of considering the sampling input delay and its sawtooth structure characteristics, a modified augmented Lyapunov-Krasovskii functional (LKF) is constructed on account of the free-matrix-based integral inequality (FMBII) together with generalized free-weighting-matrix (GFWM) inequality, which can reduce the conservatism of H∞ performance criteria. Thirdly, the expected estimator gain matrix can be designed in the light of the solution to linear matrix inequalities (LMIs). Finally, an numerical example is given to check the superiority of the proposed MSNNs control design technique.

Further improved results on non-fragile H∞ performance state estimation for delayed static neural networks

This work investigates the non-fragile H∞ state estimation issue for static neural networks (SNNs) with mixed time-varing delays and randomly occurring uncertainties (ROUs). ROUs with Bernoulli distributed white noise sequences are firstly considered for tackling state estimation of SNNs, which are mutually uncorrelated stochastic variables. In order to take full advantage of the slope information about activation function (SIAAF), the estimation error of activation function is separated into two parts. Based on the more SIAAF, a modified Lyapunov-Krasovskii functional (LKF) is constructed. In addition, by combining integral inequality and zero equality with several parameters, further improved results are emerged to ensure the error system is globally asymptotically stable with a prescribed level γ and reduce conservativeness to some extent. Furthermore, the more practical non-fragile estimator gain matrix can be obtained via the above designed optimization algorithm. Finally, two numerical examples are furnished to verify the effectiveness and performance of the developed method.

Oblique Projection and Cepstral Subtraction in Signal Subspace Speech Enhancement for Colored Noise Reduction

In this paper, a subspace speech enhancement method handling the case of colored noise using oblique projection in the cepstral domain is proposed. Perceptual features and variance normalization are used to reduce the residual noise and improve the intelligibility of the output speech. Initially, the additive noise present in the noisy speech is removed by removing the orthogonal noise subspace from the noisy speech subspace to obtain the speech subspace. Then, the oblique projection of the noise subspace on the speech subspace along the additive noise subspace is used to determine the colored noise that remains. Colored noise removal is performed by power spectral subtraction in the cepstral domain. The spectral domain constrained estimator that incorporates the combined masking property of the human auditory system is employed to estimate the clean speech signal using the variance of the colored noise. To avoid the occurrence of any abrupt spikes in the output, variance normalization is performed by adaptively changing the control parameter of the estimator's gain matrix. The spectrograms, the objective measures and the subjective intelligibility test show the superior performance of the proposed method over the other existing speech enhancement methods.