H-infinity Filter Research Articles

Robust H-infinity filtering for uncertain discrete-time systems using parameter-dependent Lyapunov functions

This paper deals with H-infinity filtering of discrete-time systems with polytopic uncertainties. The uncertain parameters are supposed to reside in a polytope. By using the parameter-dependent Lyapunov function approach and introducing some slack matrix variables, a new sufficient condition for the H-infinity filter design is presented in terms of solutions to a set of linear matrix inequalities (LMIs). In contrast to the existing results for H-infinity filter design, the main advantage of the proposed design method is the reduced conservativeness. An example is provided to demonstrate the effectiveness of the proposed method.

Nonlinear robust H-infinity filtering for a class of uncertain systems via convex optimization

A new approach for robust H-infinity filtering for a class of Lipschitz nonlinear systems with time-varying uncertainties both in the linear and nonlinear parts of the system is proposed in an LMI framework. The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multi-objective optimization. The resulting H-infinity filter guarantees asymptotic stability of the estimation error dynamics with exponential convergence and is robust against nonlinear additive uncertainty and time-varying parametric uncertainties. Explicit bounds on the nonlinear uncertainty are derived based on norm-wise and element-wise robustness analysis.

Target tracking based on the extended H-infinity filter in wireless sensor networks

In this paper, we propose a new target tracking approach for wireless sensor networks (WSNs) by using the extended H-infinity filter. First, the extended H-infinity filter for nonlinear discrete-time systems is deduced through the Krein space analysis scheme. Then, the proposed extended H-infinity filtering algorithm is applied to target tracking in wireless sensor networks. Finally, experiments are conducted through a small wireless sensor network test-bed. Both experimental and simulation results illustrate that the extended H-infinity filtering algorithm is more accurate to track a moving target in wireless sensor networks than using the extended Kalman filter in the case of having no knowledge of the statistics of the environment and the target to be tracked.

Delay-dependent robust H-infinity filtering for uncertain linear systems with time-varying interval delay

This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay. The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results. The key step in the method was to construct a special type of Lyapunov functional for the filter design problem. Unlike the existing techniques, the proposed method employed neither free weighting matrices nor any model transformation, leading to reduced computational demand as well as improved performance. Numerical examples were given to demonstrate the effectiveness of the proposed method.

Parameter and State Estimation of an Anaerobic Digestion Model in Laboratory and Pilot-Scale Conditions

AbstractThis work considers the parameter and state estimation of a low-order model of anaerobic digestion of cattle dung. First, on the basis of a previously identified parameter set, partial parameter estimation with laboratory experimental data is performed. A modern numerical sensitivity analysis, to our knowledge not used for microbial biotechnology models so far, is a successful part of the estimation procedure. Second, the estimation results are validated with pilot-scale experimental data and can be considered satisfactory. Third, state estimation of the main AD variables is made via H-infinity filtering.

Using a H∞ filter assimilation procedure to estimate root zone soil water content

AbstractRoot zone soil water content impacts plant water availability, land energy and water balances. Because of unknown hydrological model error, observation errors and the statistical characteristics of the errors, the widely used Kalman filter (KF) and its extensions are challenged to retrieve the root zone soil water content using the surface soil water content. If the soil hydraulic parameters are poorly estimated, the KF and its extensions fail to accurately estimate the root zone soil water. The H‐infinity filter (HF) represents a robust version of the KF. The HF is widely used in data assimilation and is superior to the KF, especially when the performance of the model is not well understood. The objective of this study is to study the impact of uncertain soil hydraulic parameters, initial soil moisture content and observation period on the ability of HF assimilation to predict in situ soil water content. In this article, we study seven cases. The results show that the soil hydraulic parameters hold a critical role in the course of assimilation. When the soil hydraulic parameters are poorly estimated, an accurate estimation of root soil water content cannot be retrieved by the HF assimilation approach. When the estimated soil hydraulic parameters are similar to actual values, the soil water content at various depths can be accurately retrieved by the HF assimilation. The HF assimilation is not very sensitive to the initial soil water content, and the impact of the initial soil water content on the assimilation scheme can be eliminated after about 5–7 days. The observation interval is important for soil water profile distribution retrieval with the HF, and the shorter the observation interval, the shorter the time required to achieve actual soil water content. However, the retrieval results are not very accurate at a depth of 100 cm. Also it is complex to determine the weighting coefficient and the error attenuation parameter in the HF assimilation. In this article, the trial‐and‐error method was used to determine the weighting coefficient and the error attenuation parameter. After the first establishment of limited range of the parameters, ‘the best parameter set’ was selected from the range of values. For the soil conditions investigated, the HF assimilation results are better than the open‐loop results. Copyright © 2010 John Wiley & Sons, Ltd.

Decentralized Fuzzy $H_{\infty}$ Filtering for Nonlinear Interconnected Systems With Multiple Time Delays

In general, due to the interaction among subsystems, it is difficult to design an Hinfinity filter for nonlinear interconnected systems. This paper introduces a decentralized Hinfinity fuzzy filter design for nonlinear interconnected systems with multiple time delays via T-S fuzzy models. The T-S fuzzy model consists of N time-delay T-S fuzzy subsystems. The decentralized Hinfinity filter is designed based on this model, which the asymptotic stability and a prescribed Hinfinity performance index are guaranteed for the overall filtering error system. A sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible. A simulation example is given to show the effectiveness of this approach.

H<SUB align=right>∞ filtering design for network control systems with jump parameters

The problem of robust h-infinity filtering design for networked control systems with Markovian jump parameters and packets lost is considered. A wider class of parameter uncertainties than norm-bounded parameter uncertainties is described in this model. Sufficient conditions for the filter to satisfy prescribed h-infinity performance are given in terms of LMIs, which can stabilise the system and guarantee a prescribed h-infinity performance for all admissible parameter uncertainties. A numerical example is given to illustrate the feasibility and effectiveness of the developed technique.

Robust H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump

This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump. Based on the extended Ito stochastic differential formula, sufficient conditions for the solvability of these problems are obtained. Furthermore, It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

Robust H-infinity filtering for time-delay systems with missing measurements: a parameter-dependent approach

Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.

Robust data assimilation in hydrological modeling – A comparison of Kalman and H-infinity filters

Hydrological model and observation errors are often non-Gaussian and/or biased, and the statistical properties of the errors are often unknown or not fully known. Thus, determining the true error covariance matrices is a challenge for data assimilation approaches such as the most widely used Kalman filter (KF) and its extensions, which assume Gaussian error nature and need fully known error statistics. This paper introduces H-infinite filter (HF) to hydrological modeling and compares HF with KF under various model and observation error conditions. HF is basically a robust version of KF. When model performance is not well known, or changes unpredictably, HF may be preferred over KF. HF is especially suitable for the cases where the estimation performance in the worst error case needs to be guaranteed. Through the application of HF to a hypothetical hydrologic model, this paper shows that HF is less sensitive to the uncertainty in the initial condition, corrects system bias more effectively, and converges to true state faster after interruptions than KF. In particular, HF performs better in dealing with instant human inputs (irrigation is used as an example), which are characterized by non-stationary, non-Gaussian and not fully known errors. However HF design can be more difficult than KF design due to the sensitivity of HF performance to design parameters (weights for model and observation error terms). Through sensitivity analysis, this paper shows the existence of a certain range of those parameters, in which the “best” value of the parameters is located. The tuning of HF design parameters, which can be based on users’ prior knowledge on the nature of model and observation errors, is critical for the implementation of HF.

Sampled-Data Filtering Framework for Cardiac Motion Recovery: Optimal Estimation of Continuous Dynamics From Discrete Measurements

Quantitative and noninvasive estimation of cardiac kinematics has significant physiological and clinical implications. In this paper, a sampled-data filtering framework is presented for the recovery of cardiac motion and deformation functions from periodic medical image sequences. Cardiac dynamics is a continuously evolving physical/physiological process, whereas the imaging data can provide only sampled measurements at discrete time instants. Given such a hybrid paradigm, stochastic multiframe filtering frameworks are constructed to couple the continuous dynamics with the discrete measurements, and to coordinately deal with the parameter uncertainty of the biomechanical constraining model and the noisy nature of the imaging data. The state estimates are predicted according to the continuous-time biomechanically constructed state equation between observation time points, and then updated with the new imaging-derived measurements at discrete time instants, yielding physically more meaningful and more accurate estimation results. Both continuous-discrete Kalman filter and sampled-data Hinfinity filter are applied for motion recovery. While Kalman filter is the optimal estimator under Gaussian noises, the Hinfinity scheme can give robust estimation results when the types and levels of model uncertainties and data disturbances are not available a priori. The strategies are validated through synthetic data experiments to illustrate their advantages and on canine MR phase contrast images and human MR tagging data to show their clinical potential.

Dual ${H}_{\infty}$ Algorithms for Signal Processing— Application to Speech Enhancement

This paper deals with the joint signal and parameter estimation for linear state-space models. An efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual Kalman filters. In that case, the driving process and the observation noise in the state-space representation for each filter must be white with known variances. These conditions, however, are too strong to be always satisfied in real cases. To relax them, we propose a new approach based on two dual Hinfin filters. Once a new observation of the disturbed signal is available, the first Hinfin algorithm uses the latest estimated parameters to estimate the signal, while the second Hinfin algorithm uses the estimated signal to update the parameters. In addition, as the Hinfin filter behavior depends on the choice of various weights, we present a way to recursively tune them. This approach is then studied in the following cases: (1) consistent estimation of the AR parameters from noisy observations and (2) speech enhancement, where no a priori model of the additive noise is required for the proposed approach. In each case, a comparative study with existing methods is carried out to analyze the relevance of our solution.

Computational Improvement of the Fast <formula formulatype="inline"> <tex>${\rm H}_{\infty}$</tex></formula> Filter Based on Information of Input Predictor

A computationally reduced version of the fast Hinfin filter (FHF) is derived under the assumption that the input signal to the unknown system can be represented by an autoregressive (AR) model whose order M is much lower than the filter length N. The resulting filter, referred to as the predictor-based fast Hinfin filter (P-FHF), has a computational requirement of 3N+O(M) multiplications per iteration, which is considerably lower than the requirement for the FHF if is sufficiently smaller than N . The validity of the P-FHF are confirmed by computer simulations.

Robust Fuzzy Filter Design for a Class of Nonlinear Stochastic Systems

This paper describes the robust Hinfin fuzzy filtering design for a class of nonlinear stochastic systems. The system dynamic is modelled by Itocirc-type stochastic differential equations. For general nonlinear stochastic systems, the Hinfin filter can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonlinear Hamilton-Jacobi inequality. In this paper, using fuzzy approach [Takagi-Sugeno (T-S) fuzzy model], the Hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities (LMIs) instead of a second-order Hamilton-Jacobi inequality. When the worst-case fuzzy disturbance is considered, a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error. The near minimum variance fuzzy filtering problem under the worst-case fuzzy disturbance is also characterized in terms of linear matrix inequality problem (LMIP), which can be efficiently solved by the convex optimization techniques. Simulation examples are provided to illustrate the design procedure and expected performance

Delay-dependent ℋ ∞ filtering for uncertain time delay nonlinear systems: an LMI approach

The problem of designing a delay-dependent robust Hinfin filter for time delay Takagi-Sugeno fuzzy models is considered. The purpose is to design delay-dependent Hinfin filters ensuring a prescribed Hinfin performance level for the estimation error, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of a delay-dependent Hinfin filter are given in terms of linear matrix inequalities. Membership functions' (MFs) structural information is incorporated into the delay-dependent filter design to reduce the conservativeness of neglecting this information. It is shown that incorporating MFs' structural information into the filter design does not lead to bilinear matrix inequalities, as in the control design case. Finally, a numerical example is used to illustrate the effectiveness of the proposed design techniques.

Mode-Independent ${\cal H}_{\infty}$ Filters for Markovian Jump Linear Systems

This note addresses the problem of Hinfin filtering for continuous-time linear systems with Markovian jumping parameters. The main contribution of the note is to provide a method for designing an asymptotically stable linear time-invariant Hinfin filter for systems where the jumping parameter is not accessible. The cases where the transition rate matrix of the Markov process is either exactly known, or unknown but belongs to a given polytope, are treated. The robust Hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a Lyapunov function that depends on the uncertain parameters is developed. The proposed filter designs are given in terms of linear matrix inequalities

Delay-dependent H-infinity filtering for neutral time-delay systems

This paper deals with the robust delay-dependent H-infinity filtering problem for neutral delay differential systems. The resulting filter is of the Luenberger observer type, and it guarantees that the filtering systems remains asymptotically stable and satisfies a prescribed H-infinity performance level. The Lyapunov stability theory and the descriptor model transformation are used for analysis of the system and are expected to be least conservative as compared with existing design methods. Some examples are provided to demonstrate the validity of proposed design approach.

Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements

In this paper, the robust Hinfin filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed Hinfin performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust Hinfin filter is also given. An optimization problem is subsequently formulated by optimizing the Hinfin filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

Vibration control of flexible structures using a combined H-infinity filter approach

A new approach that combines #00 control with eigenstructure assignment is proposed and applied to the vibration control of flexible structures. As the design requirements of the H^ control problem are given in the frequency domain, it is difficult for HOQ control to attain the requirements of response properties in the time domain. Eigenstructure assignment is one of the approaches that can satisfy the requirements in the time domain. A two-step approach is proposed; that is, as a first step the full state feedback control law is designed to satisfy the good response using eigenstructure assignment, and as the next step, the robust state estimator holding its performance is solved as the H^ filter problem. The proposed approach is applied to the vibration control of flexible structures, and it is demonstrated that the designed control law has good performance and robust stability by the simulation and experiments.