Quantized Measurements Research Articles

Diffusion Bias-Compensated RLS Estimation with Quantized Measurements over Adaptive Networks

We study the problem of distributed bias-compensated recursive least-squares (BCRLS) estimation with quantized measurements, which means that the nodes in adaptive networks collaborate to estimate a common deterministic parameter using quantized data. Traditional recursive least-squares (RLS) algorithms are biased when both the regressor and the output response are corrupted by stationary additive noise. And considering the limited bandwidth resources and the growing complexity in communication, the measurements transmitted in adaptive networks are always quantized in practical cases, which also contributes to the bias in estimation. Therefore, a distributed bias-compensated RLS algorithm is proposed in this paper to estimate the bias caused by both the background noise and the quantization noise and compensate for it cooperatively. Meanwhile, considering the advantages of diffusion strategies, the algorithm is developed in a diffusion fashion. Simulation results illustrate the good performance of the proposed algorithm.

Asynchronous Filtering for Discrete-Time Fuzzy Affine Systems With Variable Quantization Density.

This paper is concerned with the problem of asynchronous H∞ filtering for a class of discrete-time Takagi-Sugeno fuzzy affine systems against time-varying signal transmission delays and measurement quantization. The asynchrony refers to the situation that the plant state and the filter state belong to different local state space regions, and the quantization density can be adjusted to satisfy different performance requirements at different time instants. By transforming the filtering error system into an input-output form consisting of two interconnected subsystems, sufficient conditions on the existence of the desired asynchronous filter are established via the scaled small gain theorem to ensure that the closed-loop system is asymptotically stable with a prescribed H∞ performance index with the aid of a novel piecewise Lyapunov-Krasovskii functional and the S -procedure approach. Finally, a practical example of cart-pendulum with a modified model is provided to illustrate the effectiveness of the obtained theoretical results.

Adaptive Stabilization of Linear Systems Through a Two-Way Channel with Limited Capacity

The paper is devoted to adaptive feedback stabilization for linear time-invariant control systems with saturated quantized measurements and control. The quantization occurs due to the finite capacity of the discrete-time two-way channel connecting the plant and the controller. An adaptive controller based on the Yakubovich’s recursive goal inequalities method is designed. The bound for the minimum channel capacity sufficient to stabilize any stabilizable system with unknown parameters is evaluated for any prespecified compact set of unknown parameters.

Adaptive control of passifiable linear systems with quantized measurements and bounded disturbances

We consider a linear uncertain system with an unknown bounded disturbance under a passification-based adaptive controller with quantized measurements. First, we derive conditions ensuring ultimate boundedness of the system. Then we develop a switching procedure for an adaptive controller with a dynamic quantizer that ensures convergence to a smaller set. The size of the limit set is defined by the disturbance bound. Finally, we demonstrate applicability of the proposed controller to polytopic-type uncertain systems and its efficiency by the example of a yaw angle control of a flying vehicle.

Robust quantized H∞ filtering for discrete-time uncertain systems with packet dropouts

This paper considers the problem of H∞ filtering for uncertain discrete-time systems with quantized measurements and packet dropouts. The time-invariant uncertain parameters are supposed to reside in a polytope. The system measurement outputs are quantized by a memoryless logarithmic quantizer before being transmitted to the filter and the performance of packet dropouts is described by Bernoulli random binary distribution. Attention is focused on the design of H∞ filter to mitigate the effects of quantization and packet dropouts, which ensured not only stochastically stability but also a prescribed H∞ noise attenuation level. Via parameter-dependent Lyapunov function approach and introducing some slack variables, sufficient conditions for the existence of an H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Two examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Hybrid Control of a Bioreactor With Quantized Measurements

We consider the problem of global stabilization of an unstable bioreactor model (e.g., for anaerobic digestion), when the measurements are discrete and in finite number (“quantized”), with control of the dilution rate. The measurements define regions in the state space, and they can be perfect or uncertain (i.e., without or with overlaps). We show that, under appropriate assumptions, a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion. If the assumptions are not fulfilled, sliding modes may appear, and the transition graphs are not deterministic.

Passive filter design for periodic stochastic systems with quantized measurements and randomly occurring nonlinearities

In this paper, the passive filter is designed for periodic stochastic systems with quantized measurements and randomly occurring nonlinearities. According to the dynamic properties of periodic systems, an N-periodic density quantizer is proposed to make full use of the communication capacity. By using Bernoulli processes, a new model is introduced to describe the randomly occurring nonlinearities, where each component of the state appears nonlinearity independently, and they influence each other based on the coupling matrices B(k). A reduced-order filter is designed to reduce the computation burden. Then sufficient conditions are established to ensure that the filtering error system is stochastically stable and satisfies the passivity. Finally, the effectiveness of the proposed new design technique is illustrated via a numerical example.

Mode‐independent H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements

SummaryThis paper is concerned with the problem of H∞ filtering for discrete‐time Markov jump linear system with parametric uncertainties and quantized measurements, when the jumping mode information is not accessible. By converting the quantized errors into a sector‐bounded nonlinearity, the parametric uncertainties and measurements quantization are dealt with in a unified framework. The mode‐independent H∞ filter is designed, and sufficient conditions are established via Lyapunov function approach, such that for all possible uncertain parameters and quantization errors, the resulting filtering error system is robustly stochastically stable and achieves a guaranteed H∞ filtering error performance index. A numerical example is provided to demonstrate the feasibility and effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

Fault-Tolerant Sliding-Mode-Observer Synthesis of Markovian Jump Systems Using Quantized Measurements

This paper investigates the design problem of sliding mode observer (SMO) using quantized measurements for a class of Markovian jump systems against actuator faults. Such a problem arises in modern networked-based digital systems, where data have to be transmitted and exchanged over a digital communication channel. In this paper, a new descriptor SMO approach using quantized signals is presented, in which a discontinuous input is synthesized to reject actuator faults by an offline static compensation of quantization effects. It is revealed that the lower bound on the density of a logarithmic quantizer is 1/3, under which the quantization effects could be compensated completely by using the SMO approach. Based on the proposed observer method, the asymptotical estimations of state vector and quantization errors can be obtained simultaneously. Finally, an example of a linearized model of an F-404 aircraft engine system is included to show the effectiveness of the presented observer design method.

$$H_{\infty }$$ H ∞ Estimation for Markovian Jump Neural Networks With Quantization, Transmission Delay and Packet Dropout

This paper is concerned with the problem of robust $$H_{\infty }$$Hź estimation for a class of Markovian jump neural networks with norm-bounded parameter uncertainties, time-varying delay and limited communication capacity including signal transmission delay, measurement quantization and data packet dropout, which occur simultaneously in the same networked control system framework. Our objective is to design mode-dependent $$H_{\infty }$$Hź filter in the network environment in order to ensure the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed $$H_{\infty }$$Hź norm level for the limited communication capacity and for all admissible uncertainties. We use the delay system method to deal with signal transmission delay and data packet dropout, utilize the sector bound approach to handle measurement quantization. We also construct a comprehensive stochastic Lyapunov---Krasovskii functional to show the inherent mode-dependent state delays in the neural networks itself and the network-induced signal transmission delay. The free-weighting matrix technique and a set of strict linear matrix inequalities are employed to derive novel conditions for the desired mode-dependent $$H_{\infty }$$Hź filter. A numerical example is provided to verify the effectiveness and usefulness of the obtained main results.

A gradient flow approach to quantization of measures

In this paper we study a gradient flow approach to the problem of quantization of measures in space dimension one. By embedding our problem in L2, we find a continuous version of this problem corresponding to the limit as the number of atoms in the approximating measure tends to infinity. Under some suitable regularity assumptions on the density, we prove uniform stability and quantitative convergence results for the discrete and continuous dynamics.

Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures

Assuming a separation property, we determine the quantization dimension D(μ) of a recurrent self-similar measure μ with respect to the geometric mean error, and prove that D(μ) coincides with the Hausdorff dimension dimH⁎(μ) of μ.

Iterative learning control for discrete‐time systems with quantised measurements

In this study, the problem of iterative learning control (ILC) for discrete-time systems with quantised output measurements is considered. Here, a logarithmic quantiser is introduced and an ILC scheme is constructed by using output signals with only a finite number of quantisation levels. By using sector bound method to deal with the quantisation error, a learning condition of ILC that guarantees the convergence of tracking error is derived through rigorous analysis. It is shown that the convergence condition is determined by quantisation level, and the tracking error converges to a bound depending on quantisation density. Furthermore, the extension from linear systems to non-linear systems is also addressed. Finally, two illustrative examples are presented to demonstrate the theoretical results for both linear and non-linear systems.

H∞ filter design for fuzzy systems with quantized measurements

This paper addresses the problem of H∞ filtering for a class of discrete time T–S model based fuzzy systems with quantized measurements. The measurement signal is quantized by a logarithmic quantizer. By using basis dependent Lyapunov function, a sufficient condition is provided to ensure the stability of the filtering error system and to guarantee a given H∞ performance level. Based on this analysis result of the filtering error system, an explicit filter design approach is proposed and the basis dependent filtering algorithm is further improved by using a kind of relaxed technique. Two numerical examples are also presented to show that the filtering algorithm based on the basis dependent Lyapunov function has less conservative than the one based on the basis independent Lyapunov function.

Fault-tolerant filter design with quantized measurements

In this paper, a novel approach is proposed for designing fault-tolerant filters for linear discrete-time systems whose measurements undergo quantization. Two types of faults are considered: internal faults which are modelled by uncertainties in state space parameters; and actuator faults such as offset and stuck which are modelled as an unknown disturbance on the states. The proposed filter consists of two robust filters which operate in two different zones. These zones are defined based on the effects of the quantization on the residual signal between the quantized measurement and the one generated by the filter. Using an LMI-based approach with prescribed H∞ performance, stability LMIs are derived for the proposed dual-zone filter and finally the results are validated through simulation examples.

Data-driven Filter Design for Linear Systems with Quantized Measurements

This paper is concerned with the problem of data-driven filter design for linear systems with bounded noise by using quantized measurements. Since the mathematical model of the plant studied is unavailable, most of the existing model-based filter design approaches cannot be used to solve this problem. Another challenge lies in the fact that all the measurement data accessible is quantized. To solve this issue, a quasi-feasible filter set within the set membership framework is proposed, and a data-driven optimal worst-case filter is designed. Furthermore, an l2-l∞ almost-optimal worst-case filter design algorithm is presented by means of linear programming technique. A numerical example is given to illustrate the effectiveness of the proposed algorithms.

Medical Image Encryption and Compression Scheme Using Compressive Sensing and Pixel Swapping Based Permutation Approach

This paper presents a solution to satisfy the increasing requirements for secure medical image transmission and storage over public networks. The proposed scheme can simultaneously encrypt and compress the medical image using compressive sensing (CS) and pixel swapping based permutation approach. In the CS phase, the plain image is compressed and encrypted by chaos-based Bernoulli measurement matrix, which is generated under the control of the introduced Chebyshev map. The quantized measurements are then encrypted by permutation-diffusion type chaotic cipher for the second level protection. Simulations and extensive security analyses have been performed. The results demonstrate that at a large scale of compression ratio the proposed cryptosystem can provide satisfactory security level and reconstruction quality.

Node Topology Effect on Target Tracking Based on UWSNs Using Quantized Measurements.

On one hand, due to the energy and bandwidth constraint of underwater wireless sensor networks (UWSNs), local data quantization/compression is not only a necessity, but also an integral part of the design of UWSNs; on the other hand, since underwater nodes provide measurements for target tracking based on UWSNs, node topology, which is made up of the underwater nodes, may affect the performance of target tracking. This paper studies the effect of node topology on the target tracking in UWSNs using quantized measurements. Firstly, by using the knowledge of geometry, the effects of four typical topologies on target tracking using quantized measurements are analyzed qualitatively. The four typical topologies include two nodes are close to each other, three nodes are close to each other, three nodes are co-linear, and three nodes form a regular triangle. Secondly, under the condition of quantized measurements, the relationship between the posterior Cramer-Rao lower bound (PCRLB) and node's position is derived to evaluate the arbitrary topology. Thirdly, our target tracking scheme consisting of the optimal topology selection scheme by minimizing PCRLB, the optimal fusion center selection scheme by minimizing energy consumption, and the multisensor particle filter with quantized measurements is designed. Last, simulation results show the effectiveness of the proposed scheme.

Fault Detection for Discrete Systems With Network-Induced Nonlinearities

This paper addresses the fault detection filtering issue for a class of discrete system with network-induced nonlinear characteristics. The communication limitations, including measurements quantization, signal transmission delay, and data packet dropout, frequent in many practical networked control systems (NCSs) are considered. By transforming the residual system into an input-output form consisting two interconnected subsystems via a two-term approximation to the state delay variables, sufficient conditions are established. Under these conditions, the residual system is stochastically stable with a prescribed $\mathcal{H}_{\infty}$ level with the help of the scaled small gain (SSG) theorem developed for stochastic systems. Furthermore, the fault detection filter design approach is presented. A numerical example is also provided to demonstrate the effectiveness of the proposed method.

H ∞ filtering for Markovian jump delay systems with parameter uncertainties and limited communication capacity

This study investigates the problem of robust H ∞ filter design for a class of Markovian jump time-varying delay systems with parameter uncertainties and limited communication capacity. The parameter uncertainties are norm bounded and the communication limitations include measurement quantisation, signal transmission delay and data packet dropout, which appear simultaneously in a networked control system framework. The authors aim to design mode-dependent H ∞ filter in the network environment so as to ensure the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed H ∞ -norm level for all admissible uncertainties and the limited communication capacity. The delay system method is used to cope with signal transmission delay and data packet dropout, and the sector bound approach is introduced to treat measurement quantisation. A stochastic Lyapunov-Krasovskii function is proposed to reflect the inherent mode-dependent state delays in the system itself, the network-induced signal transmission delay and data packet dropout, the free-weighting matrix technique and a set of strict linear matrix inequalities are utilised to derive novel conditions that guarantee the desired mode-dependent H ∞ filter can be constructed. A numerical example, a vertical take-off and landing helicopter system and a mass-spring system are presented to illustrate the effectiveness and usefulness of the main results obtained.