Quantized Measurements Research Articles

Neural‐Network‐Based Finite‐Horizon Estimation for Complex Networks With Probabilistic Quantizations and Sensor Faults

ABSTRACTIn this article, the problem of finite‐horizon state estimation is studied for a class of time‐varying complex networks with sensor faults. The phenomenon of measurement quantization is considered such that the measurements are quantized probabilistically before transmitted to the state estimator. To deal with the unknown sensor fault, a neural network is introduced to appropriate the sensor fault whose weights are updated based on estimation error and the gradient descent method. Our aim is to design state estimators so that the state estimation errors are finite‐time bounded. First, sufficient conditions are established to ensure the existence of the desired state estimators. Then, the gains of the state estimators are derived in terms of the solutions to a set of recursive matrix inequalities. Finally, the usefulness of our estimation approach is confirmed by an illustrative example.

Distributed adaptive moving horizon estimation for multi-sensor networks subject to quantization effects

This paper investigates the distributed state estimation problem for multi-sensor networks with quantized measurements. Within the Bayesian framework, a distributed adaptive moving horizon estimation algorithm is developed. Unlike the existing methods regarding quantized errors roughly as bounded uncertainties, the posterior distributions of the errors are demanded to be derived. To overcome the difficulty of evaluating the posterior distributions for series of the states and quantized errors jointly, the variational Bayesian methodology is adopted to approximate the true distributions. Based on the fixed-point iteration method, the update rules are analytically derived, with the convergence criterion provided. Furthermore, by incorporating the average consensus algorithm into the prediction process, all sensors can achieve consensus on their estimates in a distributed manner. Finally, a numerical example of target tracking under logarithmic and uniform quantization effects is given to illustrate the validity of the proposed algorithm.

Unscented-Kalman-Filter-Based Remote State Estimation for Complex Networks With Quantized Measurements and Amplify-and-Forward Relays.

In this article, the remote estimation problem is addressed for a class of discrete-time complex networks under the influence of probabilistic quantization and amplify-and-forward (AF) relays. The underlying complex network model, which is inherently nonlinear and stochastic, is affected by additive process and measurement noises. Owing to the limited bandwidth of the transmission channel, the measurement outputs are quantized by a probabilistic quantizer prior to transmission. To enhance the signal quality over long-distance transmissions, the quantized measurements are sent to AF relays and subsequently forwarded to the estimator. Utilizing the unscented Kalman filter approach, a novel state estimator is designed to minimize an upper bound on the estimation error covariance. Moreover, sufficient conditions are derived to ensure that the estimation error is exponentially bounded in the mean-square sense. Lastly, the efficacy of the proposed scheme is illustrated through numerical simulations.

Simultaneous compensation of input delay and state/input quantization for linear systems via switched predictor feedback

We develop a switched predictor-feedback law, which achieves global asymptotic stabilization of linear systems with input delay and with the plant and actuator states available only in (almost) quantized form. The control design relies on a quantized version of the nominal predictor-feedback law for linear systems, in which quantized measurements of the plant and actuator states enter the predictor state formula. A switching strategy is constructed to dynamically adjust the tunable parameter of the quantizer (in a piecewise constant manner), in order to initially increase the range and subsequently decrease the error of the quantizers. The key element in the proof of global asymptotic stability in the supremum norm of the actuator state is derivation of solutions’ estimates combining a backstepping transformation with small-gain and input-to-state stability arguments, for addressing the error due to quantization. We extend this result to the input quantization case and illustrate our theory with a numerical example.

Quantized output-feedback control of piecewise-affine systems with reachable regions of quantized measurements

This article explores the asymptotic stability and output-feedback control issues of discrete-time piecewise-affine (PWA) systems under multi-input–multi-output (MIMO) quantization. Our work features more general and practical than those previous works focusing on single-input–single-output quantization for output-feedback control of PWA systems. We choose a PWA output-feedback controller adapting to the located region of the quantized measurement. Since the measurement outputs generally contain partial state information, the determination of the located region of the quantized measurement depends on the region where the system state dwells. Thus, the controller can operate within a reduced number of regions compared to the PWA system. The leveraged Lyapunov function incorporates the region information for both the state and the quantized measurement, as well as the MIMO quantization uncertainties. We propose a method for determining the reachable regions of the quantized measurement, based on which we conduct the stability analysis and output-feedback controller implementation subsequently. In consequence, both the conservativeness and the computational burden can be alleviated compared with the previous results that incorporated all the operating regions for output-feedback controller design. Finally, our proposed control methodology is tested via a water-tank control problem to validate its competence and strengths.

A Convolutional Neural Network-Based Quantization Method for Block Compressed Sensing of Images.

Block compressed sensing (BCS) is a promising method for resource-constrained image/video coding applications. However, the quantization of BCS measurements has posed a challenge, leading to significant quantization errors and encoding redundancy. In this paper, we propose a quantization method for BCS measurements using convolutional neural networks (CNN). The quantization process maps measurements to quantized data that follow a uniform distribution based on the measurements' distribution, which aims to maximize the amount of information carried by the quantized data. The dequantization process restores the quantized data to data that conform to the measurements' distribution. The restored data are then modified by the correlation information of the measurements drawn from the quantized data, with the goal of minimizing the quantization errors. The proposed method uses CNNs to construct quantization and dequantization processes, and the networks are trained jointly. The distribution parameters of each block are used as side information, which is quantized with 1 bit by the same method. Extensive experiments on four public datasets showed that, compared with uniform quantization and entropy coding, the proposed method can improve the PSNR by an average of 0.48 dB without using entropy coding when the compression bit rate is 0.1 bpp.

A distributed state and fault estimation scheme for state-saturated systems with quantized measurements over sensor networks

This article explores a new framework of distributed state and fault estimation (DSFE) for the state-saturated systems over sensor networks. To this aim, the upper bound on estimation error covariance (EEC) is ensured and the explicit expression of the corresponding estimator gains is given with both quantization effects and state saturations. Further, a feasible upper bound is located on EEC and minimized by parameterizing the estimator gain. The matrix simplification technique is adopted to deal with the sensor network topology’s sparseness problem. Additionally, the estimation performance is first analyzed and then ensured by conducting a sufficient condition. At last, experiments are carried out to verify the feasibility of the developed DSFE method.

Self-error learning framework-based algorithm for parameter recovery of extended Wiener–Hammerstein systems subject to quantised measurements

In this study, a novel estimation scheme is proposed for identifying extended Wiener–Hammerstein systems with hysteresis nonlinearity subject to quantised measurements. The proposed scheme is established in a self-error learning framework to achieve high-performance parameter estimation compared with classic error feedback learning estimation algorithms. Initially, the useful identification data can be extracted from contaminated system data by introducing an adaptive filter. Then, with the help of the filtered data, the identification error expression used to establish the estimator is derived. Subsequently, an online compensation estimation error variable is proposed to eliminate the effect of the regression vector on the convergence performance. A new adaptive law is designed with adaptive recursive gain, considering the compensation estimation error data and parameter initial error data. Under general persistent excitation (PE) condition, the PE condition of the regressor information is verified online, and the estimator convergence is strictly proven. Finally, the statistical results of two illustrated examples and a real-word example are provided to validate the positive features and effectiveness of the proposed estimation scheme.

Fusion estimation against mixed network attacks for systems with random parameter matrices, correlated noises, and quantized measurements

This paper is concerned with the information fusion estimation problems for stochastic uncertain systems with quantized measurements and mixed network attacks including random deception attack and denial-of-service (DoS) attack. The cross-correlated random parameter matrices and addictive noises simultaneously exist in the studied system. By resorting to the optimal prediction compensation mechanism for DoS attack, an optimal centralized fusion filter in the linear minimum variance sense is proposed using an innovation analysis approach. In addition, the Kalman-like recursive distributed optimal linear fusion predictor and filter without feedback are presented based on local estimators from single-sensor subsystems. The estimation error cross-covariance matrices between two arbitrary local estimators, and those between local and prior fusion estimators are derived. They have good flexibility due to the parallel structure. However, they have lower accuracy than the centralized fusion estimators. To further improve the estimation accuracy, the distributed optimal linear fusion predictor and filter with feedback are also presented. They avoid the calculation of cross-covariance matrices. Moreover, it has been mathematically proved that they have the same estimation accuracy as the centralized fusion estimators. A simulation example demonstrates the effectiveness of the proposed algorithms.

Sequential Fusion Estimation for Multirate Complex Networks With Uniform Quantization: A Zonotopic Set-Membership Approach.

In this article, the sequential fusion estimation problem is investigated for multirate complex networks (MRCNs) with uniformly quantized measurements. The process and measurement noises, which are unknown-yet-bounded (UYB), are restrained into a family of zonotopes, and the multiple sensors are allowed to have different sampling periods. To facilitate digital transmissions, the sensor measurements are uniformly quantized before being sent to the remote estimator. The purpose of this article is to design a sequential set-membership estimator such that, in the simultaneous presence of UYB noises, multirate samplings, and uniform quantization effects, the estimation error (after each measurement update) is confined to a zonotope with minimum F -radius at each time instant. By introducing certain virtual measurements, the MRCNs are first transformed into single-rate ones exhibiting a switching phenomenon. Then, by utilizing the properties of zonotopes, the desired zonotopes are derived, which contain the estimation error dynamics after each measurement update. Subsequently, the gain matrices of the sequential estimator are derived by minimizing the F -radii of these zonotopes, and the uniform boundedness is analyzed for the F -radius of the zonotope containing the estimation error after all measurement updates. Furthermore, sufficient conditions are derived to ensure the existence of the desired uniform upper/lower bounds. Finally, an illustrated example is proposed to show the effectiveness of the proposed sequential fusion estimation method.

Disorder-resistant fusion estimator design for nonlinear stochastic systems in the presence of measurement quantization

In this paper, we thoroughly study a new nonlinear disorder-resistant fusion estimation problem under both packet disorder and measurement quantization. Packet disorder, which occurs due mainly to random transmission delays (RTDs), are characterized via a series of integer-valued functions and random variables obeying certain distributions. Sensor measurements are logarithmically quantized before entering designated communication networks. The upper bounds on the filtering error covariances are acquired and later minimized by appropriately designing gain parameters of both local and fusion estimators. For fusion estimation, all local estimates and filtering covariances are integrated at a fusion center through the well-known federated criterion. Moreover, the fusion performance is examined by means of assessing the resistance of the designed estimator against the RTD-induced disorder. Simulation examples are presented to illustrate the applicability of the proposed disorder-resistant fusion estimator.

Fuzzy membership-function-dependent design of aperiodic sample-data control scheme for nonlinear PMSG-based WECS with quantization measurements via refined looped Lyapunov functional

This manuscript investigates the fuzzy memory sampled-data control (MSDC) scheme for the nonlinear permanent magnet synchronous generator (PMSG)-based wind energy conversion system (WECS) with quantization measurements. First, due to the complex nonlinearity, a Takagi-Sugeno (T-S) fuzzy modeling approach is successfully applied to the dynamics of nonlinear PMSG-based WECS. Second, by using the information of both quantized aperiodic sampling pattern and signal transmission delay, an H∞-based fuzzy quantized controller is put forward to ensure the stable performance as well as disturbance suppression index of the considered PMSG model by utilizing the refined looped Lyapunov functional (RLLF) approach. This RLLF perfectly utilizes more realistic information about the time derivative of the fuzzy membership function and actual sampling pattern. Then, two new integral inequalities are introduced to approximate the quadratic integral terms arising from the derivative of RLLF. Next, we establish some less conservative stabilization results in terms of linear matrix inequalities (LMIs) using the constructed RLLF, along with the proposed integral inequalities and fuzzy membership function-dependent (MFD) switching ideas. Finally, the simulation studies of PMGS-based WECS are validated numerically, and then a comparative example is provided to emphasize the superiority and relevance of the suggested approach.

Set Membership State Estimation with Quantized Measurements and Optimal Threshold Selection

The problem of state estimation with quantized measurements is addressed in the set membership estimation setting. The main contribution concerns the optimal selection of the quantizer thresholds in order to minimize the worst-case radius of the feasible state set. This allows one to design adaptive quantizers reducing the uncertainty associated to the state estimates. The proposed solution is applied to several outer approximations of the feasible sets, based on parallelotopes, zonotopes and constrained zonotopes. The benefits of the threshold selection mechanism are assessed on a numerical example, highlighting the trade off between computational burden and uncertainty reduction.

Further Results on Asynchronous Fuzzy Observer-Based Output Feedback Control for Networked Nonlinear Systems Using Quantized Measurements

Further Results on Asynchronous Fuzzy Observer-Based Output Feedback Control for Networked Nonlinear Systems Using Quantized Measurements

Asynchronous Quantized Control of Piecewise-Affine Systems

This technical note proposes a novel asynchronous control approach for discrete-time piecewise-affine (PWA) systems with logarithmic quantization of both multi-inputs and multi-state measurements. Since the actual system state and the quantized state may not always be in the same operating region due to quantization-induced uncertainties, the operating modes of the PWA system and the controller which depends on the quantized states may be asynchronous. Aiming at reducing the computational cost and the conservatism of the results, a mapping region-based algorithm is first proposed to determine the reachable dwelling regions for the quantized state. By using a convex combination model to approximate the quantization-induced uncertainties, a novel piecewise Lyapunov function taking into consideration the uncertainties is then proposed. It is shown that with the newly proposed Lyapunov function, the desired asynchronous controller can be obtained and the resulting closed-loop system is asymptotically stable. A simulated chemical reactor example is presented to illustrate the effectiveness and the superiority of the proposed asynchronous control approach.

Zonotopic set-membership estimation for time-varying systems subject to dynamical biases and quantization effects

In this paper, the zonotopic set-membership estimation (SME) problem is studied for time-varying systems subject to dynamical biases and uniform quantization. The considered dynamical bias evolves according to a certain dynamic process disturbed by unknown-but-bounded noises. The main objective of the paper is to propose a zonotopic SME method such that the real states are included in zonotopes described by linear image of an unit hypercube. By analyzing the dynamics of biases and states, the intersection set containing the state are first obtained based on the quantization measurements. Then, an auxiliary zonotope is constructed to bound the intersection where the center and generator matrix are presented recursively. Through orchestrating the correlation matrix, the F-Radius of such an auxiliary zonotope is further minimized. To reduce the computational burden, the desired zonotope with finite-dimensional generator matrix is constructed to externally approximate the auxiliary zonotope. Furthermore, the boundedness stability is analyzed for the developed zonotopic SME approach in the simulations presence of dynamical biases and uniform quantization. Finally, an example is provided to display the effectiveness of the SME method.

Robust Packetized MPC for Networked Systems Subject to Packet Dropouts and Input Saturation With Quantized Feedback.

This article develops a robust packetized predictive control framework to deal with the quantized-feedback control problem of networked systems subject to Markovian packet dropouts and input saturation. In the proposed framework, the Markov chain model of packet dropout is established from the link of the controller to the actuator. To deal with the quantized measurements, a robust packetized predictive control method is presented with a quantized-feedback law. The problem of unreliable transmission is addressed by proposing a packet dropout compensation strategy with a forgetting factor. An augmented Markovian jump system model is established to take the packet dropouts into account. The synthesis of packetized predictive control is then developed by minimizing a worst case cost function with respect to the model uncertainties. The recursive feasibility of the proposed controller design problem and the mean-square stability of the closed-loop systems are proved, respectively. The proposed packetized predictive control method is demonstrated by simulating a four-tank process system.

Adaptive Neural Network-Based Observer Design for Switched Systems With Quantized Measurements.

This study is concerned with the adaptive neural network (NN) observer design problem for continuous-time switched systems via quantized output signals. A novel NN observer is presented in which the adaptive laws are constructed using quantized measurements. Then, persistent dwell time (PDT) switching is considered in the observer design to describe fast and slow switching in a unified framework. Accurate estimations of state and actuator efficiency factor can be obtained by the proposed observer technique despite actuator degradation. Finally, a simulation example is provided to illustrate the effectiveness of the developed NN observer design approach.

Parsimonious system identification from fragmented quantised measurements

Quantisation is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantised observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantised realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a ℓ p , ( 0 < p < 1 ) , quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the ℓ 1 minimisation in terms of the sparsity of the induced solution.

Dissipative Asynchronous Filtering for Networked Fuzzy Markov Jumping Systems With Quantized Measurements and Packet Dropouts

This article is concerned with the dissipative asynchronous filtering for a class of networked Takagi–Sugeno fuzzy Markov jumping systems subject to packet dropouts. The system measurements are quantized with a logarithmic quantizer and a Bernoulli model is introduced to deal with the packet dropouts occurred in the communication channel from the quantizer to the filter. Both the quantizer and the filter are mode dependent, and their modes are asynchronous with those of the physical plant, governed by two hidden Markov models. Based on the mode-and fuzzy-rule-dependent Lyapunov function method, a sufficient condition is derived such that the resultant filtering error system is stochastically stable in the mean-square sense and strictly dissipative. The slack-matrix approach and Finsler’s lemma are further exploited to design suitable dissipative filters if a set of linear matrix inequalities are feasible. Finally, two examples including a tunnel-diode circuit system are taken to demonstrate the efficiency of our proposed results.