Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany

An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series

Copyright [2009] 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 extended Kalman filter (EKF) algorithm is applied to model the gene regulatory network from gene time series data. The gene regulatory network is considered as a nonlinear dynamic stochastic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EKF algorithm for identifying both the model parameters and the actual value of gene expression levels. It is shown that the EKF algorithm is an online estimation algorithm that can identify a large number of parameters (including parameters of nonlinear functions) through iterative procedure by using a small number of observations. Four real-world gene expression data sets are employed to demonstrate the effectiveness of the EKF algorithm, and the obtained models are evaluated from the viewpoint of bioinformatics

Simultaneous state and actuator fault estimation for satellite attitude control systems

AbstractIn this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The simulation results show satisfactory performance in estimating states and actuator faults. It also shows that multiple faults can be estimated successfully

A nonlinear Luenberger-like observer for nonlinear singular systems

International audienceThis paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs. We firstly regularize the singular system by injecting the derivative of outputs into the system. Then differential geometric method is applied to transform the regularized system into a simple normal form, for which a Luenberger-like observer is proposed

State/noise estimator for descriptor systems with application to sensor fault diagnosis

For descriptor systems with measurement output noises (input disturbances may exist at the same time), a new descriptor estimator technique is developed. The necessary and sufficient condition for the existence of the present estimator is derived, and a systematic design approach is addressed. The effect of uncertainties is decoupled completely, and the asymptotic estimates of the descriptor system state and the output noise are obtained simultaneously. Furthermore, a normal state/disturbance estimator is also given. For a class of nonlinear descriptor systems with both output noises and input uncertainties, a nonlinear descriptor estimator is derived by using the proposed design approach, together with the linear matrix inequality technique. The existence and convergence of the nonlinear descriptor estimator is proven. The asymptotic estimates of the descriptor nonlinear system state and the output noise are obtained at the same time. The present estimators are applied to the sensor fault diagnosis, and hence the sensor fault can be estimated asymptotically. Finally, two numerical examples are included to illustrate the proposed design procedures and applications

Observer based active fault tolerant control of descriptor systems

The active fault tolerant control (AFTC) uses the information provided by fault detection and fault diagnosis (FDD) or fault estimation (FE) systems offering an opportunity to improve the safety, reliability and survivability for complex modern systems. However, in the majority of the literature the roles of FDD/FE and reconfigurable control are described as separate design issues often using a standard state space (i.e. non-descriptor) system model approach. These separate FDD/FE and reconfigurable control designs may not achieve desired stability and robustness performance when combined within a closed-loop system.This work describes a new approach to the integration of FE and fault compensation as a form of AFTC within the context of a descriptor system rather than standard state space system. The proposed descriptor system approach has an integrated controller and observer design strategy offering better design flexibility compared with the equivalent approach using a standard state space system. An extended state observer (ESO) is developed to achieve state and fault estimation based on a joint linear matrix inequality (LMI) approach to pole-placement and H∞ optimization to minimize the effects of bounded exogenous disturbance and modelling uncertainty. A novel proportional derivative (PD)-ESO is introduced to achieve enhanced estimation performance, making use of the additional derivative gain. The proposed approaches are evaluated using a common numerical example adapted from the recent literature and the simulation results demonstrate clearly the feasibility and power of the integrated estimation and control AFTC strategy. The proposed AFTC design strategy is extended to an LPV descriptor system framework as a way of dealing with the robustness and stability of the system with bounded parameter variations arising from the non-linear system, where a numerical example demonstrates the feasibility of the use of the PD-ESO for FE and compensation integrated within the AFTC system.A non-linear offshore wind turbine benchmark system is studied as an application of the proposed design strategy. The proposed AFTC scheme uses the existing industry standard wind turbine generator angular speed reference control system as a “baseline” control within the AFTC scheme. The simulation results demonstrate the added value of the new AFTC system in terms of good fault tolerance properties, compared with the existing baseline system

Unknown input observer approaches to robust fault diagnosis

This thesis focuses on the development of the model-based fault detection and isolation /fault detection and diagnosis (FDI/FDD) techniques using the unknown input observer (UIO) methodology. Using the UI de-coupling philosophy to tackle the robustness issue, a set of novel fault estimation (FE)-oriented UIO approaches are developed based on the classical residual generation-oriented UIO approach considering the time derivative characteristics of various faults. The main developments proposed are:- Implement the residual-based UIO design on a high fidelity commercial aircraft benchmark model to detect and isolate the elevator sensor runaway fault. The FDI design performance is validated using a functional engineering simulation (FES) system environment provided through the activity of an EU FP7 project Advanced Fault Diagnosis for Safer Flight Guidance and Control (ADDSAFE).- Propose a linear time-invariant (LTI) model-based robust fast adaptive fault estimator (RFAFE) with UI de-coupling to estimate the aircraft elevator oscillatory faults considered as actuator faults.- Propose a UI-proportional integral observer (UI-PIO) to estimate actuator multiplicative faults based on an LTI model with UI de-coupling and with added H∞ optimisation to reduce the effects of the sensor noise. This is applied to an example on a hydraulic leakage fault (multiplicative fault) in a wind turbine pitch actuator system, assuming that thefirst derivative of the fault is zero. - Develop an UI–proportional multiple integral observer (UI-PMIO) to estimate the system states and faults simultaneously with the UI acting on the system states. The UI-PMIO leads to a relaxed condition of requiring that the first time derivative of the fault is zero instead of requiring that the finite time fault derivative is zero or bounded. - Propose a novel actuator fault and state estimation methodology, the UI–proportional multiple integral and derivative observer (UI-PMIDO), inspired by both of the RFAFE and UI-PMIO designs. This leads to an observer with the comprehensive feature of estimating faults with bounded finite time derivatives and ensuring fast FE tracking response.- Extend the UI-PMIDO theory based on LTI modelling to a linear parameter varying (LPV) model approach for FE design. A nonlinear two-link manipulator example is used to illustrate the power of this method

Fault tolerant control for nonlinear aircraft based on feedback linearization

The thesis concerns the fault tolerant flight control (FTFC) problem for nonlinear aircraft by making use of analytical redundancy. Considering initially fault-free flight, the feedback linearization theory plays an important role to provide a baseline control approach for de-coupling and stabilizing a non-linear statically unstable aircraft system. Then several reconfigurable control strategies are studied to provide further robust control performance:- A neural network (NN)-based adaption mechanism is used to develop reconfigurable FTFC performance through the combination of a concurrent updated learninglaw. - The combined feedback linearization and NN adaptor FTFC system is further improved through the use of a sliding mode control (SMC) strategy to enhance the convergence of the NN learning adaptor. - An approach to simultaneous estimation of both state and fault signals is incorporated within an active FTFC system.The faults acting independently on the three primary actuators of the nonlinear aircraft are compensated in the control system.The theoretical ideas developed in the thesis have been applied to the nonlinear Machan Unmanned Aerial Vehicle (UAV) system. The simulation results obtained from a tracking control system demonstrate the improved fault tolerant performance for all the presented control schemes, validated under various faults and disturbance scenarios.A Boeing 747 nonlinear benchmark model, developed within the framework of the GARTEUR FM-AG 16 project “fault tolerant flight control systems”,is used for the purpose of further simulation study and testing of the FTFC scheme developed by making the combined use of concurrent learning NN and SMC theory. The simulation results under the given fault scenario show a promising reconfiguration performance

Verkopplungsbasierte Methoden zum Regler- und Beobachterentwurf für nichtlineare Deskriptorsysteme

Bei der modularen Modellbildung dynamischer Systeme entsteht direkt und intuitiv eine differential-algebraische Beschreibungsform. In der regelungstechnischen Literatur wird diese meist als Deskriptorsystem bezeichnet. Die Interpretation eines nichtlinearen Deskriptorsystems als spezielles Verkopplungsproblem bildet die Grundlage für die in der vorliegenden Arbeit hergeleiteten Methoden. Dafür wird der aus der Zustandsraummethodik bekannte Verkopplungsentwurf genutzt, um für ein Deskriptorsystem ein verkoppeltes Zustandssystem zu berechnen. Dieses verkoppelte Zustandssystem existiert für alle regulären Deskriptorsysteme, insbesondere auch für solche mit differenzierendem Verhalten, und ist geeignet, die Lösung des Deskriptorsystems zu reproduzieren. Die verkoppelte Zustandsraumdarstellung stellt außerdem die Basis sowohl für Regler- als auch Beobachterentwürfe dar, wobei die besondere Herausforderung darin besteht, die Regler und Beobachter auf das Deskriptorsystem zu übertragen und vor allem immer ein geregeltes Deskriptorsystem zu erzeugen, welches regulär ist. Auf diesem Weg lassen sich für Zustandssysteme bekannte Methoden auf nichtlineare Deskriptorsysteme überführen. Unter der Angabe neuer notwendiger und hinreichender Bedingungen können Deskriptorsysteme sowohl statisch als auch dynamisch entkoppelt werden, unabhängig davon, ob sie differenzierendes Verhalten besitzen. Die Untersuchung der Entkopplungsregelung führt darüber hinaus auf neue invariante Kennzahlen für Deskriptorsysteme, den maximalen Differenzordnungen. Daneben wird die Nulldynamik eines Deskriptorsystems allgemein definiert, wodurch Aussagen über eine stabile Entkopplung möglich sind. Die exakte Deskriptorlinearisierung überführt ein Deskriptorsystem durch Deskriptorrückführung und Koordinatentransformation in ein lineares Deskriptorsystem. Für die Berechnungen sind im Allgemeinen partielle Differentialgleichungen zu lösen. Die in einem Sonderfall mögliche analytische Lösung kann dagegen direkt angegeben werden. Mit einem zeitvarianten Verkopplungsregler gelingt es außerdem, einen Riccatiregler für lineare, zeitvariante Deskriptorsysteme zu entwerfen. Neben dem Reglerentwurf für Deskriptorsysteme ist das verkoppelte Zustandssystem auch für die Definition und Überprüfung der Beobachtbarkeit geeignet. Der Beobachterentwurf für ein Deskriptorsystem führt im Allgemeinen auf ein dynamisches System, welches wieder ein Deskriptorsystem ist. Existiert ein Beobachter in Zustandsdarstellung, so wird das Deskriptorsystem als kausal beobachtbar bezeichnet. Für die kausale Beobachtbarkeit werden nicht nur neue notwendige und hinreichende Bedingungen hergeleitet, sondern auch ein Methode, die den Entwurf immer in einen Zustandsbeobachterentwurf für ein beobachtbares Zustandssystem überführt. Alle neuen Methoden werden außerdem auf lineare Deskriptorsysteme angewandt. Gerade die dort mögliche Transformation in den Laplacebereich ermöglicht ein einfacheres Verständnis der Ergebnisse. Die praktische Anwendbarkeit der theoretischen Methoden zeigen die Beispielsysteme am Ende der Arbeit. Die neuen Verfahren werden sowohl an Simulationsbeispielen als auch an einem realen Versuchsstand implementiert und validiert