具有随机协议网络化系统的H∞滤波

本文研究了一类具有随机介质访问协议网络化系统的H∞滤波问题.将传感器和滤波器的通信过程描述为一个马尔可夫链,进而将滤波误差系统建模成一个马尔可夫跳变系统.然后,运用李雅普诺夫方法和线性矩阵不等式技术,给出了滤波误差系统随机稳定且具有给定H∞性能的一个充分条件,并基于该条件给出了H∞滤波器的设计方法.最后的数值算例验证了本文方法的有效性.     

Risk-sensitive filtering for discrete-time systems with time-varying delay

In this paper, the risk-sensitive filtering problem with time-varying delay is investigated. The problem is transformed into Krein space as an equivalent optimisation problem. The observations with time-varying delays are restructured as ones with multiple constant delays by defining a binary variable model with respect to the arrival process of observations, containing the same state information as the original. Finally, the reorganised innovation analysis approach in Krein space allows the solution to the proposed risk-sensitive filtering in terms of the solutions to Riccati and matrix difference equations.     

Nonlinear filtering for systems with random structure

This note studies the nonlinear filtering problem for a linear system with random structure governed by a finite state Markov process. A characterization of the optimal mean-square filter is derived and some suboptimal filter approximations are presented.     

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.     

Variance-constrained filtering for uncertain stochastic systems with missing measurements

In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.     

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.     

Robust filtering for a class of nonlinear stochastic systems with probability constraints

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method.     

Optimal filtering for linear state delay systems

In this note, the optimal filtering problem for linear systems with state delay over linear observations is treated proceeding from the general expression for the stochastic Ito differential of the optimal estimate and the error variance. As a result, the optimal estimate equation similar to the traditional Kalman-Bucy one is derived; however, it is impossible to obtain a system of the filtering equations, that is closed with respect to the only two variables, the optimal estimate and the error variance, as in the Kalman-Bucy filter. The resulting system of equations for determining the error variance consists of a set of equations, whose number is specified by the ratio between the current filtering horizon and the delay value in the state equation and increases as the filtering horizon tends to infinity. In the example, performance of the designed optimal filter for linear systems with state delay is verified against the best Kalman-Bucy filter available for linear systems without delays and two versions of the extended Kalman-Bucy filter for time-delay systems.     

具有可变时滞的中立型随机系统的渐近性质

本文研究了一类具有可变时滞的中立型随机系统解的渐近性质.利用Lyapunov函数It、^o公式和上鞅收敛定理,得到了该系统解的一些几乎必然渐近稳定性与p阶均值渐近稳定性、几乎必然多项式渐近稳定性与p阶均值多项式渐近稳定性及几乎必然指数稳定性与p阶均值指数稳定性的充分判据.与经典的随机稳定性结论相比,本文所建立的判据充分利用了随机扰动项的作用,无须LV(扩散算子)的负定.     

Optimal filtering for networked systems with stochastic sensor gain degradation

In this paper, the optimal filtering problem is investigated for a class of networked systems in the presence of stochastic sensor gain degradations. The degradations are described by sequences of random variables with known statistics. A new measurement model is put forward to account for sensor gain degradations, network-induced time delays as well as network-induced data dropouts. Based on the proposed new model, an optimal unbiased filter is designed that minimizes the filtering error variance at each time-step. The developed filtering algorithm is recursive and therefore suitable for online application. Moreover, both currently and previously received signals are utilized to estimate the current state in order to achieve a better accuracy. A numerical simulation is exploited to illustrate the effectiveness of the proposed algorithm.     

Linear filtering for bilinear stochastic differential systems with unknown inputs

Investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance, whose statistics are completely unknown.. A linear filter is proposed, based on a suitable decomposition of the state of the bilinear system into two components. The first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm. No a priori information on the disturbance is required for the filter implementation. The proposed filter is robust with respect to the unknown input, in that the covariance of the estimation error is not affected by such input. Numerical simulations show the effectiveness of the proposed filter.     

Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises

In this note, a minimum entropy filtering algorithm is presented for a class of multivariate dynamic stochastic systems, which are represented by a set of time-varying difference equations and are subjected to the multivariate non-Gaussian stochastic inputs. Several new concepts including the hybrid random vector, hybrid probability and hybrid entropy are firstly established to describe the probabilistic property of the estimation errors. New relationships are provided between the probability density functions (PDFs) of the multivariate stochastic input and output for different mapping cases. Recursive algorithms are then proposed to design the real-time sub-optimal filter so that the hybrid entropy of the estimation error can be minimized. Finally, an improved algorithm is provided through the on-line tuning of the weighting matrices so as to guarantee the local stability of the error system.     

Optimal filtering in stochastic discrete-time systems with unknowninputs

In this note we derive a recursive filtering algorithm for the linear discrete-time dynamic system with indeterminate-stochastic inputs. The algorithm is based on the minimax-optimal method of parameter estimation in the linear regression model with parameters of two different types: unknown and stochastic with partially known characteristics     

Robust H∞ filtering of stochastic time‐delay systems with state dependent noise

This paper is concerned with the H_∞ filtering design for discrete‐time stochastic time‐delay systems with state dependent noise. A sufficient condition for the existence of H_∞ filter design is presented via linear matrix inequalities. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay

This paper investigates output-feedback control for a class of stochastic high-order nonlinear systems with time-varying delay for the first time. By introducing the adding a power integrator technique in the stochastic systems and a rescaling transformation, and choosing an appropriate Lyapunov-Krasoviskii functional, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.     

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 H∞ sliding mode control scheme for uncertain fractional stochastic systems: Nonlinear analysis and design

This paper investigates the $H_{\infty }$ sliding mode control (SMC) design for fractional stochastic systems. We study a very general category of stochastic systems that are nonlinear and driven by fractional Brownian motion (fBm). A robust $H_{\infty }$ SMC scheme is presented for a fractional stochastic model with external disturbance, state- and disturbance-dependent noise, and uncertainties, which ensures that the closed-loop system is stochastically stable. We propose a novel sliding surface and then prove its reachability in the state space. Furthermore, the conditions for the stochastic stability of the sliding motion are derived via nonlinear Hamilton–Jacobi (HJ)-type inequalities. In addition, an $H_{\infty }$ SMC method is developed for a special class of fractional stochastic models, and two sets of linear matrix inequality (LMI) conditions are obtained, which are sufficient for stochastic stability. Eventually, the validity of the results is validated via a simulation example.     

BIBO stabilization of stochastic delay systems with uncertainty

Employing the Razumikhin technique, we present several criteria of input-to-bounded state stabilization and bounded-input-bounded-output stabilization in mean square for nonlinear and quasi-linear stochastic control systems with time-varying delay and time-varying uncertainties.