Robust H∞ filtering for discrete nonlinear stochastic systems with time-varying delay

This is the postprint version of the article. The official published version can be accessed from the link below - © 2007 Elsevier IncIn this paper, we are concerned with the robust H∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under study involves parameter uncertainties, stochastic disturbances, time-varying delays and sector-like nonlinearities. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is constrained to be robustly asymptotically stable in the mean square, and a prescribed H∞ disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. These conditions are dependent on the lower and upper bounds of the time-varying delays. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality (LMI). Finally, a numerical example is exploited to show the usefulness of the results derived.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the National Natural Science Foundation of China (60774073 and 10471119), the NSF of Jiangsu Province of China (BK2007075 and BK2006064), the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, and the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002

Fiscal shocks and real exchange rate dynamics: Some evidence for Latin America

This paper analyses the effects of fiscal shocks using a two-country macroeconomic model for output, labour input, government spending and relative prices which provides the orthogonality restrictions for obtaining the structural shocks. Dynamic simulation techniques are then applied, in particular to shed light on the possible effects of fiscal imbalances on the real exchange rate in the case of six Latin American countries. Using quarterly data over the period 1980-2006, we find that in a majority of cases fiscal shocks are the main driving force of real exchange rate fluctuations

Fiscal Shocks and Real Exchange Rate Dynamics: Some Evidence for Latin America

This paper analyses the effects of fiscal shocks using a two-country macroeconomic model for output, labour input, government spending and relative prices which provides the orthogonality restrictions for obtaining the structural shocks. Dynamic simulation techniques are then applied, in particular to shed light on the possible effects of fiscal imbalances on the real exchange rate in the case of six Latin American countries. Using quarterly data over the period 1980-2006, we find that in a majority of cases fiscal shocks are the main driving force of real exchange rate fluctuations.fiscal shocks, real exchange rate, Latin American countries

Robust fault detection for vehicle lateral dynamics: Azonotope-based set-membership approach

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksIn this work, a model-based fault detection layoutfor vehicle lateral dynamics system is presented. The majorfocus in this study is on the handling of model uncertainties andunknown inputs. In fact, the vehicle lateral model is affectedby several parameter variations such as longitudinal velocity,cornering stiffnesses coefficients and unknown inputs like windgust disturbances. Cornering stiffness parameters variation isconsidered to be unknown but bounded with known compactset. Their effect is addressed by generating intervals for theresiduals based on the zonotope representation of all possiblevalues. The developed fault detection procedure has been testedusing real driving data acquired from a prototype vehicle.Index Terms— Robust fault detection, interval models,zonotopes, set-membership, switched uncertain systems, LMIs,input-to-state stability, arbitrary switching.Peer ReviewedPostprint (author's final draft

Long Run And Cyclical Dynamics In The Us Stock Market

This paper examines the long-run dynamics and the cyclical structure of the US stock market using fractional integration techniques. We implement a version of the tests of Robinson (1994a), which enables one to consider unit roots with possibly fractional orders of integration both at the zero (long-run) and the cyclical frequencies. We examine the following series: inflation, real risk-free rate, real stock returns, equity premium and price/dividend ratio, annually from 1871 to 1993. When focusing exclusively on the long-run or zero frequency, the estimated order of integration varies considerably, but nonstationarity is found only for the price/dividend ratio. When the cyclical component is also taken into account, the series appear to be stationary but to exhibit long memory with respect to both components in almost all cases. The exception is the price/dividend ratio, whose order of integration is higher than 0.5 but smaller than 1 for the long-run frequency, and is between 0 and 0.5 for the cyclical component. Also, mean reversion occurs in all cases. Finally, we use six different criteria to compare the forecasting performance of the fractional (at both zero and cyclical frequencies) models with others based on fractional and integer differentiation only at the zero frequency. The results show that the former outperform the others in a number of cases

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

Fault detection and isolation for linear dynamic systems

As modern control systems and engineering processes become increasingly more complex and integrated, the consequences of system failures and faults can be disastrous environmentally and economically. This thesis considers the fault detection and isolation (FDI) problem for linear time-invariant (LTI) systems subject to faults, disturbances and model uncertainties. Firstly, a novel on-line approach to the robust FDI problem for linear discrete-time systems is proposed by using input/output measurement analysis over a finite estimation horizon. Upper and lower bounds on the fault signal are computed at each sampling instant so that a fault is detected and isolated when its upper bound is smaller than zero or its lower bound is larger than zero. Moreover, a subsequent-state-estimation technique, together with an estimation horizon update procedure are given to allow the on-line FDI process to be repeated in a moving horizon scheme. Secondly, an optimal solution to theH−/H∞ fault detection (FD) problem is given for linear time-invariant systems subject to faults, disturbances and model uncertainties by using an observer-based approach. A new performance index is developed to capture both fault detection and disturbance rejection requirements which is particularly suitable for handling model uncertainties. A class of optimal solutions to the problem is then given in the form of simple linear matrix inequalities (LMI) with two degrees of freedom. By appropriately choosing these degrees of freedom, fault isolation can also be achieved. Thirdly, in order to improve the FD performance and remove restrictive rank assumptions, routinely made in the literature, observer-based FD problems are investigated at a single frequency and over a finite frequency range, respectively. An optimal solution is derived such that, at a given frequency, the static observer generates a residual signal which minimizes the sensitivity of the residual to disturbances while maintaining a minimum level of sensitivity to faults. Then, an initial investigation is carried out for the FD problem over a finite frequency range. A solution is derived in the form of an LMI optimization by using the generalized KYP lemma followed by a linearization procedure. Conditions under which this solution is optimal are also derived. Fully worked out numerical examples, mostly from the literature, are given to illustrate the effectiveness of all the proposed schemes