Variance-constrained multiobjective filtering for uncertain continuous-time stochastic systems

In this paper, we consider stochastic linear continuous-time systems subject to parameter uncertainties affecting both system dynamics and noise statistics. A linear filter is used to estimate a linear combination of the states of the system. The problem addressed is the design of a perturbation-independent filter such that, for all admissible parameter perturbations, the following three objectives are simultaneously achieved. Firstly the filtering process is D-stable, that is, the eigenvalues of the filtering matrix are located inside a prespecified disc. Secondly the steady-state variance of the estimation error of each state is not more than the individual prespecified value. Thirdly the transfer function from exogenous noise inputs to error state outputs meets the prespecified H norm upper bound constraint. Therefore, the resulting filtering process will be provided with the expected transient property, steady-state error variance constraint and disturbance rejection behaviour, irrespective of the parameter uncertainties. An effective algebraic matrix inequality approach is developed to solve such a multiobjective H₂     

Robust state estimation for uncertain discrete-time stochastic systems with missing measurements

In this paper, results of robust estimation of Zhou (2010a) are extended to state estimation with missing measurements. A new procedure is derived which inherits the main properties of that of Zhou (2010a). In this extension, a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult. Though introducing a monotonic function and using the so-called squeeze rule, this new robust estimator is proved to converge to a stable system. Numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of Wang, Yang, Daniel, and Liu (2005).     

filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities

In this paper, we deal with the robust H_∞ filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H_∞ disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.     

Robust filtering with stochastic nonlinearities and multiple missing measurements

This paper is concerned with the filtering problem for a class of discrete-time uncertain stochastic nonlinear time-delay systems with both the probabilistic missing measurements and external stochastic disturbances. The measurement missing phenomenon is assumed to occur in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval . Such a probabilistic distribution could be any commonly used discrete distribution over the interval . The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is exponentially mean-square stable. By using the linear matrix inequality (LMI) method, sufficient conditions are established that ensure the exponential mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs. Illustrative examples are exploited to show the effectiveness of the proposed design procedures.     

Quantised polynomial filtering for nonlinear systems with missing measurements

This paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements. The nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low-order polynomial terms with norm-bounded coefficients. The transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a Bernoulli distributed sequence taking values on 0 or 1. Dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors, the quantisations as well as the missing measurements at each time instant. Such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations. The filter design algorithm is recursive and therefore applicable for online computation. An illustrative example is exploited to show the effectiveness of the proposed algorithm.     

Real-time optimal filtering for stochastic systems with multiresolutional measurements

A real-time optimal filtering algorithm for stochastic systems with multiresolutional measurements is derived. The algorithm gives fused estimates based upon all available data at a particular time index. A multiresolutional distributed filtering scheme is employed. The wavelet transform is utilized as a bridge, effectively linking different resolution levels. A tree-like hierarchical data structure introduced in this paper facilitates the real-time multiresolutional filtering.     

测量丢失概率不确定的网络化系统的鲁棒故障检测

研究一类具有测量数据丢失概率不确定的网络化系统的鲁棒故障检测问题,系统用概率属于一个区间的Bernoulli随机二进制切换序列来描述测量数据丢失.设计一个基于观测器的鲁棒故障检测滤波器(RFDF),对于区间内的每一个概率,RFDF残差误差输出对故障敏感且对具有L2有界的未知干扰输入有一定的鲁棒性,应用线性矩阵不等式方法,给出并证明了此RFDF的存在条件.最后通过例子说明了该方法的有效性.     

Minimax filtering in linear stochastic uncertain discrete-continuous systems

Filtering of the states of a system, whose dynamics is defined by an Ito stochastic differential equation, by discrete and discrete-continuous observations is studied under the assumption that the intensities of continuous noises and covariance matrices of discrete noises are known only within to membership of certain uncertainty sets. A minimax approach is used to solve the problem. The filter is optimized with an integral quality criterion. Minimax filtering equations are derived from the solution of the dual optimization problem. A numerical solution algorithm for the problem is designed. Results of numerical experiments are presented.     

Robust finite horizon minimax filtering for discrete-time stochastic uncertain systems

We study a finite-horizon robust minimax filtering problem for time-varying discrete-time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which the stochastic noises, driving the system, are defined. The optimal minimax filter has been found by applying techniques of risk-sensitive LQG control. The structure and properties of resulting filter are analyzed and compared to H_∞ and Kalman filters.     

Robust H∞ filtering for uncertain impulsive stochastic systems under sampled measurements

This paper is concerned with the problem of robust H_∞ filtering for uncertain impulsive stochastic systems under sampled measurements. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is to design a stochastically stable filter, using the locally sampled measurements, which ensures both the robust stochastic stability and a prescribed level of H_∞ performance for the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. An example is provided to demonstrate the effectiveness of the proposed approach.     

Robust H-infinity filtering on uncertain systems under sampled measurements

1 Introduction Sampled measurements systems consist of a continuous- time plant and discrete-time plant. The systems contain sig- nals that evolve in continuous time as well as signals that evolve in discrete time. It is rather difficult to apply the stan- dard analysis results for linear continuous-time systems and discrete-time systems to the analysis of sampled measure- ments systems [1]. This fact has motivated much of the re- search on the analysis and synthesis of sampled measure- ments …     

Robust filtering of stochastic uncertain systems on an infinite time horizon

In this paper, we consider a robust filtering problem for continuous time stochastic uncertain systems.The uncertainty in the system is characterized in terms of an uncertain probability distribution on the noise input. This uncertainty is assumed to satisfy a certain relative entropy constraint. The solution to a specially parameterized risk-sensitive stochastic filtering problem is used to construct a filter for the original uncertain system which guarantees an optimal worst-case filtering error. The corresponding minimax optimal filter is obtained by solving a pair of algebraic Riccati equations.     

Robust Kalman filtering for uncertain systems

This paper studies the problem of Kalman filter design for uncertain systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and measurement matrices. The problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the above problem. Furthermore, a suboptimal covariance upper bound can be computed by a convex optimization.     

Quadratic stabilization for uncertain stochastic systems

1IntroductionInthelast decades ,manyauthors studiedrobust quadraticstabilization control of deterministic linear systems withparameter uncertainty or structured uncertainty, see[1 ~8] . Robust quadratic stability and stabilization ofdeterministic systems were first introduced by [1] ,bymeans of a common Lyapunovfunction.Most earlier resultson robust quadratic stabilization,including some necessaryand sufficient conditions , were expressed in terms ofRiccati_type equations or inequalities , wh…     

Reduced-order filtering for networks with Markovian jumping parameters and missing measurements

The problem of reduced-order H _∞ filters design for Markovian jumping complex networks with polytopic time-varying transition probability matrices is first addressed in this paper, where the dynamic of each node is described by the sector-bounded nonlinearity. For the measurements, both quantisation and packet dropouts are considered, where each node has its own packet dropout rate. By using the mode- and transition probability-dependent Lyapunov function approach, two sufficient conditions are provided to ensure the stochastic stability and the disturbance attenuation performance of the resulting filtering error system. Then, the mode-independent reduced-order filters design method is proposed, and the filter parameters are given explicitly by linear matrix inequality method. Finally, the effectiveness of the theoretic results presented is illustrated via a numerical example which contains performance comparison of different mode-independent reduced-order filters.     

output feedback control for uncertain stochastic systems with time-varying delays

This paper deals with the problem of H_∞ output feedback control for uncertain stochastic systems with time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is the design of a full-order dynamic output feedback controller ensuring robust exponential mean-square stability and a prescribed H_∞ performance level for the resulting closed-loop system, irrespective of the uncertainties. A sufficient condition for the existence of such an output feedback controller is obtained and the expression of desired controllers is given.     

Resilient linear filtering of uncertain systems

The problem of resilient linear filtering for a class of linear continuous-time systems with norm-bounded uncertainties is investigated. We have considered additive filter gain variations to reflect the imprecision in filter implementation. The design problem of resilient linear filter is formulated as a convex optimization problem over linear matrix inequalities. As a limiting procedure, the case of resilient Kalman filter is derived. All the developed results are conveniently extended to the case of multiplicative filter gain variations. Simulation studies are carried out to support the theoretical findings.     

Stability of stochastic systems with uncertain time delays

For linear delay systems with bilinear noise sufficient conditions are given for the global asymptotic stochastic stability independent of the length of the delay(s). For linear stochastic noise terms, sufficient conditions for the existence of an invariant distribution, for all values of the delay are given. It is shown that the gaussian distribution is the unique invariant distribution. The covariance and correlation matrix function of the resulting stationary process are completely characterized by a Lyapunov-type equation. All these sufficient conditions are obtained in the form of the existence of some positive definite matrices satisfying certain Riccati-type equations.