Chokri Mechmeche

State Estimation for Polytopic LPV Descriptor Systems: Application to Fault Diagnosis

Abstract In this paper, the design of a polytopic Unknown Input Observer (UIO) for polytopic Linear Varying Parameter (LPV) descriptor systems is investigated. The method presented is based on the representation of affine LPV descriptor systems where parameters evolve in a hypercube domain. The considered polytopic UIO is able to estimate the states of the system in spite of the presence of unknown inputs. This approach is also applied to actuator fault detection, isolation and estimation. Stability conditions of such observer are expressed in terms of Linear Matrix Inequalities (LMI). An example illustrates the effectiveness and performances of such polytopic LPV observer.

Unknown Input Observer Design for Fuzzy Bilinear System: An LMI Approach

A new method to design a fuzzy bilinear observer (FBO) with unknown inputs is developed for a class of nonlinear systems. The nonlinear system is modeled as a fuzzy bilinear model (FBM). This kind of T-S fuzzy model is especially suitable for a nonlinear system with a bilinear term. The proposed fuzzy bilinear observer subject to unknown inputs is developed to ensure the asymptotic convergence of the error dynamic using the Lyapunov method. The proposed design conditions are given in linear matrix inequality (LMI) formulation. The paper studies also the problem of fault detection and isolation. An unknown input fuzzy bilinear fault diagnosis observer design is proposed. This work is given for both continuous and discrete cases of fuzzy bilinear models. Illustrative examples are chosen to provide the effectiveness of the given methodology.

T-S fuzzy bilinear observer for a class of nonlinear system

This paper deals with a fuzzy bilinear observer design for a class of nonlinear systems. The nonlinear system is modeled as a Takagi-Sugeno fuzzy bilinear model. The observer stability is assured irrespective of the inputs and stability conditions are expressed in terms of Linear Matrix Inequality (LMI). A numerical example is given to demonstrate the effectiveness of the proposed Takagi-Sugeno Fuzzy Bilinear Observer (T-S FBO).

Robust H ∞ fault diagnosis for multi-model descriptor systems: A multi-objective approach

A large class of engineering systems are modeled by coupled Differential and algebraic Equations (DAEs), called also singular or descriptor systems. Due to the singular nature of the algebraic equations, descriptor systems do not satisfy the standard state-space description and require special techniques. So far, the literature has concentrated mostly on the numerical analysis and control aspects of descriptor or DAEs systems. This paper investigates the problem of faults detection in nonlinear DAE systems described by a multi-model with the design of an Unknown Input Observer. The stability and robustness properties of the fault diagnosis scheme are investigated in term of LMIs. A simulation example illustrating the ability of the proposed fault diagnosis architecture to detect multiple faults is presented.

Fault Diagnosis Based on Adaptive Polytopic Observer for LPV Descriptor Systems

This paper presents an Adaptive Polytopic Observer (APO) design in order to develop a fault detection and estimation method dedicated to polytopic Linear Parameter Varying (LPV) descriptor systems under time-varying actuator faults. This paper extends a Fault Diagnosis (FD) method developed for regular LTI systems to polytopic LPV descriptor systems. The design and stability conditions of this APO are provided. The design is formulated through LMI (Linear Matrix Inequalities) techniques under equality constraints. The performances of the proposed fault detection and estimation scheme are illustrated using an electrical circuit.

A High Gain Observer based LMI Approach

This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. The observer that we consider has a constant gain and concerns a class of uniformly observable systems. A sufficient condition permitting to design such a constant gain observer is given. The calculation of this gain is based on LMI technics

Fault detection and isolation of ship electric propulsion system using residual generator

This paper deals with the design and analysis of residual generators for polynomial systems. The computation of a bank of residual generators is exploited for fault detection and isolation of a ship electric propulsion system, characterized by a nonlinear model, in the presence of disturbance. The simulation results shows how a fault de-tectability/isolability procedure can be made on a practical system.

Fault tolerant control for multi-models descriptor systems

In this paper, Fault Tolerant Control (FTC) for a class of nonlinear descriptor systems with actuator faults represented by Multi-Models approach is investigated. The proposed strategy is based on the design of Unknown Input Multi-Observer (UIMO). The considered actuator failures can be lock-in-place or loss of effectiveness. Based on Multi-model approach equipped with unknown input multi-observer to approximate the state vector of the original system and the occurred failures together, a fault tolerant control law is developed to achieve asymptotic output regulation and closed-loop stability, despite the exogenous inputs. A numerical simulation study illustrates the effectiveness of the proposed scheme.

Unknown inputs observer for energy management in an electric traction system

In this paper, a bilinear model for the DC-DC (Boost and Buck/Boost) power converters is proposed. Based on this model, a full order bilinear observer is given. To illustrate the effectiveness of the proposed observer a simulations using Matlab/simulink are carried out.