Abdelkader Akhenak

State and unknown input estimation for discrete time multiple model

This paper deals with the state estimation of nonlinear discrete systems described by a multiple model with unknown inputs. The main goal concerns the simultaneous estimation of the systems state and the unknown inputs. This goal is achieved through the design of a multiple observer based on the elimination of the unknown inputs. It is shown that the observer gains are solutions of a set of linear matrix inequalities. After that, an unknown input estimation method is proposed. An academic example and an application dealing with message decoding illustrate the effectiveness of the proposed multiple observer.

Design of sliding mode unknown input observer for uncertain Takagi-Sugeno model

This paper addresses the analysis and design of a sliding mode observer on the basis of a Takagi-Sugeno (T-S) model subject both to unknown inputs and uncertainties. The main contribution of the paper is the development of a robust observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilization of the observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of linear matrix inequalities (LMI). The validity of the proposed methodology is illustrated by an academic example.

State estimation of uncertain multiple model with unknown inputs

This paper is dedicated to the synthesis of a sliding mode multiple observer. The considered systems are represented by an uncertain (nonlinear) multiple model with unknown inputs. Stability conditions of such observers are expressed in terms of linear matrix inequalities (LMI). An example of simulation is given to illustrate the proposed method.

Sliding mode multiple observer for fault detection and isolation

This paper deals with the design of a sliding mode multiple observer (an observer based on a multiple model) allowing to estimate the state vector of a nonlinear dynamical system. This latter is influenced by unknown inputs which act on it through a known transmission matrix. The state estimation and consequently the output estimation can therefore be classically used for detecting and isolating faults.

Fault detection and isolation using sliding mode observer for uncertain Takagi-Sugeno fuzzy model

This paper addresses fault detection and isolation (FDI) problem using a sliding mode fuzzy observer on the basis of a uncertain Takagi-Sugeno (T-S) fuzzy model. First, a robust fuzzy observer with respect to the uncertainties is designed. The convergence of the fuzzy observer is performed by the search of suitable Lyapunov matrices. It is shown how to synthesis observers using a set of linear matrix inequalities (LMI) conditions. Once the fuzzy observer is designed, FDI problem for nonlinear systems described by T-S fuzzy systems using the fuzzy observer is presented. A bank of fuzzy observer is then designed in order to investigate fault diagnosis problems. The validity of the proposed methodology is illustrated on a dynamic vehicle model.

On the design of observer for unknown inputs fuzzy models

In this paper, we consider the design of an fuzzy observer for a non-linear system with unknown inputs described by a fuzzy model. The main objective is to estimate state variables of the fuzzy model subject to unknown inputs which influence states and outputs of the system simultaneously. Using the Lyapunov method and Linear Matrix Inequalities (LMI), sufficient conditions are proposed to design the proposed unknown input fuzzy observer. The pole placement in an LMI region is also considered. The validity of the proposed methodology is illustrated by an academic example.

ESTIMATION OF STATE AND UNKNOWN INPUTS OF A NONLINEAR SYSTEM REPRESENTED BY A MULTIPLE MODEL

In this paper, we consider a nonlinear system represented by a multiple model, where a part of its inputs is unknown. Our objective is to estimate the state variables and the unknown inputs of this system. For that, we propose the synthesis of a multiple observer based on the elimination of these unknown inputs. It is shown how to determine the gains of the local observers, these gains being solutions of a set of linear matrix inequalities (LMI). The model of an hydraulic system with three tanks is used to test the suggested procedure.

Design of observers for Takagi-Sugeno fuzzy models for Fault Detection and Isolation

This paper addresses the design of an unknown input fuzzy observer for Takagi-Sugeno (T-S) fuzzy model subject to unknown inputs. The main contribution of the paper is the development of a robust fuzzy observer in presence of disturbances. Based on Lyapunov function, it is shown how to determine observers gains in linear matrix inequalities (LMI). The proposed T-S observer is used for detection and isolation of faults which can affect a nonlinear models. The validity of the proposed methodology is illustrated by estimating the yaw rate and the fault of automatic steering vehicle.

Design of a sliding mode fuzzy observer for uncertain Takagi-Sugeno fuzzy model: application to automatic steering of vehicles

This paper addresses the analysis and design of a Sliding Mode Fuzzy Observer (SMFO) on the basis of a Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of a robust fuzzy observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilisation of the fuzzy observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of Linear Matrix Inequalities (LMIs). The validity of the proposed methodology is illustrated by an estimation of the yaw rate of automatic steering of vehicles.

UNKNOWN INPUT MULTIPLE OBSERVER BASED-APPROACH - APPLICATION TO SECURE COMMUNICATIONS

Abstract This paper presents multiple observer design for nonlinear chaotic systems with unknown inputs in multiple model approach. The considered unknown inputs influences the states and the outputs of the system. The main objective is to estimate the state variables as well as the unknown inputs of this system. For that, we propose the synthesis of a multiple observer based on the elimination of these unknown inputs. The synthesis conditions of the proposed multiple observer are derived in linear matrix inequalities (LMI) terms. The proposed method is applied to secure communication. An simulation example is given to illustrate the effectiveness of the proposed synthesis conditions.