On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper

Filter for detecting and isolating faults for a nonlinear system

In the paper the problem of detecting and isolating multiple faults for nonlinear systems is considered. A strategy of state filtering is derived in order to detect and isolate multiple faults which appear simultaneously or sequentially in a discrete time nonlinear systems with unknown inputs. For the considered system for which a fault isolation condition is fulfilled the proposed method can isolate p simultaneous faults with at least p+q output measurements, where q is the number of unknown inputs or disturbances. A reduced output residual vector of dimension p+q is generated and the elements of this vector are decoupled in a way that each element of the vector is associated with only one fault or unmeasured input

Framework for state and unknown input estimation of linear time-varying systems

The design of unknown-input decoupled observers and filters requires the assumption of an existence condition in the literature. This paper addresses an unknown input filtering problem where the existence condition is not satisfied. Instead of designing a traditional unknown input decoupled filter, a Double-Model Adaptive Estimation approach is extended to solve the unknown input filtering problem. It is proved that the state and the unknown inputs can be estimated and decoupled using the extended Double-Model Adaptive Estimation approach without satisfying the existence condition. Numerical examples are presented in which the performance of the proposed approach is compared to methods from literature.Comment: This paper has been accepted by Automatica. It considers unknown input estimation or fault and disturbances estimation. Existing approaches considers the case where the effects of fault and disturbance can be decoupled. In our paper, we consider the case where the effects of fault and disturbance are coupled. This approach can be easily extended to nonlinear system

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Active actuator fault-tolerant control of a wind turbine benchmark model

This paper describes the design of an active fault-tolerant control scheme that is applied to the actuator of a wind turbine benchmark. The methodology is based on adaptive filters obtained via the nonlinear geometric approach, which allows to obtain interesting decoupling property with respect to uncertainty affecting the wind turbine system. The controller accommodation scheme exploits the on-line estimate of the actuator fault signal generated by the adaptive filters. The nonlinearity of the wind turbine model is described by the mapping to the power conversion ratio from tip-speed ratio and blade pitch angles. This mapping represents the aerodynamic uncertainty, and usually is not known in analytical form, but in general represented by approximated two-dimensional maps (i.e. look-up tables). Therefore, this paper suggests a scheme to estimate this power conversion ratio in an analytical form by means of a two-dimensional polynomial, which is subsequently used for designing the active fault-tolerant control scheme. The wind turbine power generating unit of a grid is considered as a benchmark to show the design procedure, including the aspects of the nonlinear disturbance decoupling method, as well as the viability of the proposed approach. Extensive simulations of the benchmark process are practical tools for assessing experimentally the features of the developed actuator fault-tolerant control scheme, in the presence of modelling and measurement errors. Comparisons with different fault-tolerant schemes serve to highlight the advantages and drawbacks of the proposed methodology