A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s)

Robust fault estimation for stochastic Takagi-Sugeno fuzzy systems

Nowadays, industrial plants are calling for high-performance fault diagnosis techniques to meet stringent requirements on system availability and safety in the event of component failures. This paper deals with robust fault estimation problems for stochastic nonlinear systems subject to faults and unknown inputs relying on Takagi-Sugeno fuzzy models. Augmented approach jointly with unknown input observers for stochastic Takagi-Sugeno models is exploited here, which allows one to estimate both considered faults and full system states robustly. The considered unknown inputs can be either completely decoupled or partially decoupled by observers. For the un-decoupled part of unknown inputs, which still influence error dynamics, stochastic input-to-state stability properties are applied to take nonzero inputs into account and sufficient conditions are achieved to guarantee bounded estimation errors under bounded unknown inputs. Linear matrix inequalities are employed to compute gain matrices of the observer, leading to stochastic input-to-state-stable error dynamics and optimization of the estimation performances against un-decoupled unknown inputs. Finally, simulation on wind turbine benchmark model is applied to validate the performances of the suggested fault reconstruction methodologies

Observer Design for Takagi-Sugeno Descriptor System with Lipschitz Constraints

This paper investigates the design problem of observers for nonlinear descriptor systems described by Takagi-Sugeno (TS) system; Depending on the available knowledge on the premise variables two cases are considered. First a TS descriptor system with measurables premises variables are proposed. Second, an observer design which satisfying the Lipschitz condition is proposed when the premises variables are unmeasurables. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in terms of Linear Matrix Inequalities (LMIs). Examples are included to illustrate those methods.Comment: 13 pages,5 figures; International Journal of Instrumentation and Control Systems (IJICS) Vol.2, No.2, April 201

A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Copyright [2004] 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.Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked

Design of robust control for uncertain fuzzy quadruple-tank systems with time-varying delays

Producción CientíficaThe robust H∞ observer-based control design is addressed here for non-linear Takagi-Sugeno (T-S) fuzzy systems with time-varying delays, subject to uncertainties and external disturbances. This is motivated by the quadruple-tank with time delay control problem. The observer design methodology is based on constructing an appropriate Lyapunov–Krasovskii functional (LKF) for an augmented system formed from the original and the delayed states. The bilinear terms are transferred to the linear matrix inequalities, thanks to a change of variables which can be solved in one step. Furthermore, by employing the L2 performance index, the adverse effects of persistent bounded disturbances is largely avoided. The proposed method has the advantage of relating the controller and Lyapunov function to both the original and delayed states. Then, the controller and observer gains are obtained simultaneously by solving these inequalities with off-the-shelf software (Yalmip/MATLAB toolbox). Finally, an application to a simulated quadruple-tank system with time delay is carried out to demonstrate the benefits of the proposed technique, showing a compromise between controller simplicity and robustness that outperforms previous approaches.Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach

Estimation et commande des systèmes descripteurs

This thesis addresses the estimation and control for nonlinear descriptor systems. The developments are focused on a family of nonlinear descriptor models with a full-rank descriptor matrix. The proposed approaches are based on a Takagi-Sugeno (TS) descriptor representation of a given nonlinear descriptor model. This type of TS models is a generalization of the standard TS ones. One of the mains goals is to obtain conditions in terms of linear matrix inequalities (LMIs). In the existing literature, the observer design for TS descriptor models has led to bilinear matrix inequality (BMI) conditions. In addition, to the best of our knowledge, there are no results in the literature on controller/observer design for discrete-time TS descriptor models (with a non-constant and invertible descriptor matrix).Three problems have been addressed: state feedback controller design, observer design, and static output feedback controller design. LMI conditions have been obtained for both continuous and discrete-time TS descriptor models. In the continuous-time case, relaxed LMI conditions for the state feedback controller design have been achieved via parameterdependent LMI conditions. For the observer design, pure LMI conditions have been developed by using a different extended estimation error. For the static output feedback controller, LMI constraints can be obtained once an auxiliary matrix is fixed. In the discretetime case, results in the LMI form are provided for state/output feedback controller design and observer design; thus filling the gap in the literature. Several examples have been included to illustrate the applicability of the obtained results and the importance of keeping the original descriptor structure instead of computing a standard state-space.Cette thèse est consacrée au développement des techniques d’estimation et de commande pour systèmes descripteurs non linéaires. Les développements sont centrés sur une famille particulière de systèmes descripteurs non linéaires avec une matrice descripteur de rang plein. Toutes les approches présentées utilisent un formalisme de modélisation du type Takagi-Sugeno (TS) pour représenter les modèles descripteurs non linéaires. Un objectif très important est de développer des conditions sous la forme d’inégalités matricielles linéaires (LMI, en anglais). Dans la littérature, les conditions pour l’estimation des modèles TS descripteurs s’écrivent sous forme d’inégalités matricielles bilinéaires (BMI, en anglais). En plus, à notre connaissance, il n’y pas de résultats dans la littérature concernant la commande/estimation pour les modèles TS descripteurs en temps discret (avec une matrice descripteur régulière non linéaire).Trois problèmes ont été examinés : commande par retour d’état, estimation de l’état et commande statique par retour de la sortie. Dans le cas continu, des conditions moins conservatives ont été développées pour la commande par retour d’état. Pour l’estimation d’état, des conditions LMI ont été obtenues (au lieu des usuelles BMI) en utilisant un différent vecteur d’erreur augmenté. Pour la commande statique par retour de la sortie, des conditions LMI sont proposées si une matrice auxiliaire est fixée. Pour le temps discret, des nouveaux résultats sous la forme LMI ont été développées pour la commande/estimation, comblant ainsi certains manques de la littérature. Des exemples ont été inclus pour montrer l’applicabilité de tous les résultats que nous avons obtenus et ainsi l’importance de garder la structure originale des descripteurs

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Simultaneous actuator and sensor fault reconstruction of singular delayed linear parameter varying systems in the presence of unknown time varying delays and inexact parameters

In this article, robust fault diagnosis of a class of singular delayed linear parameter varying systems is considered. The considered system has delayed dynamics with unknown time varying delays and also it is affected by noise, disturbance and faults in both actuators and sensors. Moreover, in addition to the aforementioned unknown inputs and uncertainty, another source of uncertainty related to inexact measures of the scheduling parameters is present in the system. Making use of the descriptor system approach, sensor faults in the system are added as additional states into the original state vector to obtain an augmented system. Then, by designing a suitable proportional double integral unknown input observer (PDIUIO), the states, actuator, and sensor faults are estimated. The uncertainty due to the mismatch between the inexact parameters that schedule the observer and the real parameters that schedule the original system is formulated with an uncertain system approach. In the PDIUIO, the uncertainty induced by unknown inputs (disturbance, noise and actuator, and sensor faults), unknown delays, and inexact parameter measures are attenuated in H8 sense with different weights. The constraints regarding the existence and the robust stability of the designed PDIUIO are formulated using linear matrix inequalities. The efficiency of the proposed method is verified using an application example based on an electrical circuit.Peer ReviewedPostprint (author's final draft