Robust H-infinity filter design for uncertaintime-delay singular stochastic systems withMarkovian 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 It6 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 on uncertain systems under sampled measurements

This paper is concerned with the problem of robust H-infinity filtering on uncertain systems under sampled measurements, both continuous disturbance and discrete disturbance are considered in the systems. The parameter uncertainty is assumed to be time-varying norm-bounded. The aim is to design an asymptotically stable filter, using the locally sampled measurements, which ensures both the robust asymptotic stability and a prescribed level of H-infinity performance for the filtering error dynamics for all admissible uncertainties. The derivation process is simplified by introducing auxiliary systems and the sufficient condition for the existence of such a filter is proposed. During the study, the main results were expressed as LMIs by employing various matrix techniques. Using LMI toolbox of Matlab software, it is very convenient to obtain the appropriate filter. Finally, a numerical example shows that the method is effective and feasible.

Robust H-infinity filtering for time-delaysystems 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 H-infinity filter for a class of polytopic Delta operator systems

This study deals with the robust H-infinity filtering for a class of Delta operator systems with polytopic uncertainties. By the aid of introducing two slack matrices to eliminate the coupling between systems matrices and Lya- punov matrices, an improved version of the bounded real lemma is given via linear matrix inequality formulation, which shows a close correspondence between the continuous- and discrete-time H-infinity performance criterion. Based on it, the existence condition of the desired filter is obtained such that the corresponding filtering error system is asymptotically stable with a guaranteed performance index. A numerical example is employed to illustrate the feasibility and advantages of the orooosed design.

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.

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 un- certain 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.

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.

An LMI approach to robust H-infinity control for uncertain singular time-delay systems

The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time- delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities （LMIs） involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method.

Application of ensemble H-infinity filter in aquifer characterization andcomparison to ensemble Kalman filter

Though the ensemble Kalman filter （EnKF） has been successfully applied in many areas, it requires explicit and accurate model and measurement error information, leading to difficulties in practice when only limited information on error mechanisms of observational in-struments for subsurface systems is accessible. To handle the uncertain errors, we applied a robust data assimilation algorithm, the ensemble H-infinity filter （EnHF）, to estimation of aquifer hydraulic heads and conductivities in a flow model with uncertain/correlated observational errors. The impacts of spatial and temporal correlations in measurements were analyzed, and the performance of EnHF was compared with that of the EnKF. The results show that both EnHF and EnKF are able to estimate hydraulic conductivities properly when observations are free of error; EnHF can provide robust estimates of hydraulic conductivities even when no observational error information is provided. In contrast, the estimates of EnKF seem noticeably undermined because of correlated errors and inaccurate error statistics, and filter divergence was observed. It is concluded that EnHF is an efficient assimilation algorithm when observational errors are unknown or error statistics are inaccurate.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

H-infinity鲁棒滤波增益研究

基于Krein空间状态模型,深入分析H-infinity滤波增益,提出了广义滤波增益、增益失调因子等相关概念,并给出了H-infinity滤波器鲁棒性机理及H-infinity滤波器发散原因等相关结论。在此基础上,建立了一套结构化算法,清晰地描述了H-infinity滤波的两个计算回路和两个更新过程。仿真结果证明了相关结论的正确性。

Adaptive Robust Tracking Control of Pressure Trajectory Based on Kalman Filter

When adaptive robust control（ARC） strategy based on backstepping design is applied in pneumatic servo control, accurate pressure tracking in motion is especially necessary for both force and position trajectories tracking ofrodless pneumatic cylinders, and therefore an adaptive robust pressure controller is developed in this paper to improve the tracking accuracy of pressure trajectory in the chamber when the pneumatic cylinder is moving. In the proposed adaptive robust pressure controller, off-line fitting of the orifice area and on-line parameter estimation of the flow coefficient are utilized to have improved model compensation, and meanwhile robust feedback and Kalman filter are used to have strong robustness against uncertain nonlinearities, parameter fluctuations and noise. Research results demonstrate that the adaptive robust pressure controller could not only track various pressure trajectories accurately even when the pneumatic cylinder is moving, but also obtain very smooth control input, which indicates the effectiveness of adaptive model compensation. Especially when a step pressure trajectory is tracked under the condition of the movement of a rodless pneumatic cylinder, maximum tracking error of ARC is 4.46 kPa and average tracking error is 0.99 kPa, and steady-state error of ARC could achieve 0.84 kPa, which is very close to the measurement accuracy of pressure transducer.

Robust cubature Kalman filter method for the nonlinear alignment of SINS

Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system(SINS).Cubature Kalman filter(CKF)is a popular tool for nonlinear initial alignment.Standard CKF assumes that the statics of the observation noise are pre-given before the filtering process.Therefore,any unpredicted outliers in observation noise will decrease the stability of the filter.In view of this problem,improved CKF method with robustness is proposed.Multiple fading factors are introduced to rescale the observation noise covariance.Then the update stage of the filter can be autonomously tuned,and if there are outliers exist in the observations,the update should be less weighted.Under the Gaussian assumption of KF,the Mahalanobis distance of the innovation vector is supposed to be Chi-square distributed.Therefore a judging index based on Chi-square test is designed to detect the noise outliers,determining whether the fading tune are required.The proposed method is applied in the nonlinear alignment of SINS,and vehicle experiment proves the effective of the proposed method.

Robust H_∞ Filter Design for 2D Discrete Systems in Roesser Model

This paper investigates the robust H ∞ filtering problem for uncertain two-dimensional (2D) systems described by the Roesser model. The parameter uncertainties considered in this paper are assumed to be of polytopic type. A new structured polynomially parameter-dependent method is utilized, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. A numerical example illustrates the feasibility and advantage of the proposed filter design methods.

H-infinity control for networked control systems (NCS) with time-varying delays

This paper discusses H-infinity state feedback control for a networked control system with time-varying delays. Based on the flee-weighing matrix method, a dehy-dependent stability criterion satisfying a prescribed H-infinity norm bound is presented for an NCS with unknown, time-varying and bounded delays. And then, the criterion is transformed into sufficient conditions based on linear matrix inequalities for H-infinity control. The conditions thus obtained are also used to design an H-infinity state feedback controller. This design method is further extended to solve the design problem of robust H-infinity state feedback control. A numerical example demonstrates the validity of the method.

Study on Robust H_∞ Filtering in Networked Environments

This paper is concerned with the robust H ∞ filter problem for networked environments, which are subject to both transmission delay and packet dropouts randomly. By employing random series which have Bernoulli distributions taking value of 0 or 1, the data transmission model is obtained. Based on state augmentation and stochastic theory, the sufficient condition for robust stability with H ∞ constraints is derived for the filtering error system. The robust filter is designed in terms of feasibility of one certain linear matrix inequality （LMI）, which is formed by adopting matrix congruence transformations. A numerical example is given to show the effectiveness of the proposed filtering method.

Design of parametric fault detection systems: An H-infinity optimization approach

Problems related to the design of observer-based parametric fault detection(PFD) systems are studied. The core of our study is to first describe the faults occurring in systemactuators, sensors and components in the form of additive parameter deviations, then to transformthe PFD problems into a similar additive fault setup, based on which an optimal observer-basedoptimization fault detection approach is proposed. A constructive solution optimal in the sense ofminimizing a certain performance index is developed. The main results consist of defining parametricfault detectability, formulating a PFD optimization problem and its solution. A numerical exampleto demonstrate the effectiveness of the proposed approach is provided.

Gaussian process regression-based quaternion unscented Kalman robust filter for integrated SINS/GNSS

High-precision filtering estimation is one of the key techniques for strapdown inertial navigation system/global navigation satellite system(SINS/GNSS)integrated navigation system,and its estimation plays an important role in the performance evaluation of the navigation system.Traditional filter estimation methods usually assume that the measurement noise conforms to the Gaussian distribution,without considering the influence of the pollution introduced by the GNSS signal,which is susceptible to external interference.To address this problem,a high-precision filter estimation method using Gaussian process regression(GPR)is proposed to enhance the prediction and estimation capability of the unscented quaternion estimator(USQUE)to improve the navigation accuracy.Based on the advantage of the GPR machine learning function,the estimation performance of the sliding window for model training is measured.This method estimates the output of the observation information source through the measurement window and realizes the robust measurement update of the filter.The combination of GPR and the USQUE algorithm establishes a robust mechanism framework,which enhances the robustness and stability of traditional methods.The results of the trajectory simulation experiment and SINS/GNSS car-mounted tests indicate that the strategy has strong robustness and high estimation accuracy,which demonstrates the effectiveness of the proposed method.

Robust H_∞ filtering for discrete-time systems with Markovian switching and time-delays

The robust H∞ filtering problem for uncertain discrete-time Markovian jump linear systems with mode- dependent time-delays is investigated. Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed H∞ performance level of the resulting filtering error system, for all admissible uncertainties. The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables. Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities. Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.

Unscented Transformation Based Robust Kalman Filter and Its Applications in Fermentation Process

State estimation is the precondition and foundation of a bioprocess monitoring and optimal control. However,there are many difficulties in dealing with a non-linear system,such as the instability of process, un-modeled dynamics,parameter sensitivity,etc.This paper discusses the principles and characteristics of three different approaches,extended Kalman filters,strong tracking filters and unscented transformation based Kalman filters.By introducing the unscented transformation method and a sub-optimal fading factor to correct the prediction error covariance,an improved Kalman filter,unscented transformation based robust Kalman filter,is proposed. The performance of the algorithm is compared with the strong tracking filter and unscented transformation based Kalman filter and illustrated in a typical case study for glutathione fermentation process.The results show that the proposed algorithm presents better accuracy and stability on the state estimation in numerical calculations.