Mohammed Chadli

Robust Observer Design for Unknown Inputs Takagi–Sugeno Models

This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.

H−/H∞ fault detection filter design for discrete-time Takagi–Sugeno fuzzy system

Abstract In this note, a robust fault detection observer is designed for a T–S (Takagi–Sugeno) fuzzy model with sensor faults and unknown bounded disturbances. The method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable. The idea is to formulate the robust fault detection observer design as an H − / H ∞ problem. Based on nonquadratic Lyapunov functions, a solution of the considered problem is then given via a Linear Matrix Inequality ( LMI ) formulation. An example is proposed to illustrate the design conditions.

LMI Solution for Robust Static Output Feedback Control of Discrete Takagi–Sugeno Fuzzy Models

This paper deals with the stabilization problem of discrete-time Takagi-Sugeno (T-S) fuzzy systems via static output controller (SOFC). The proposed method uses the descriptor approach to study this problem and leads to strict linear matrix inequality (LMI ) formulation. In contrast with the existing results, the method allows coping with multiple output matrices, as well as uncertainties. Moreover, the new proposed method can lead to less conservative results by introducing slack variables and considering multiple Lyapunov matrices. A robust SOFC for uncertain T-S fuzzy models is also derived in strict LMI terms. Numerical examples are given to illustrate the effectiveness of the proposed design results.

Mixed H-Infinity and Passive Filtering for Discrete Fuzzy Neural Networks With Stochastic Jumps and Time Delays

In this brief, the problems of the mixed H-infinity and passivity performance analysis and design are investigated for discrete time-delay neural networks with Markovian jump parameters represented by Takagi-Sugeno fuzzy model. The main purpose of this brief is to design a filter to guarantee that the augmented Markovian jump fuzzy neural networks are stable in mean-square sense and satisfy a prescribed passivity performance index by employing the Lyapunov method and the stochastic analysis technique. Applying the matrix decomposition techniques, sufficient conditions are provided for the solvability of the problems, which can be formulated in terms of linear matrix inequalities. A numerical example is also presented to illustrate the effectiveness of the proposed techniques.

Robust Fault Tolerant Tracking Controller Design for a VTOL aircraft

Abstract This paper deals with the fault tolerant control (FTC) design for a Vertical Takeoff and Landing (VTOL) aircraft subject to external disturbances and actuator faults. The aim is to synthesize a fault tolerant controller ensuring trajectory tracking for the nonlinear uncertain system represented by a Takagi–Sugeno (T–S) model. In order to design the FTC law, a proportional integral observer (PIO) is adopted which estimate both of the faults and the faulty system states. Based on the Lyapunov theory and ℒ 2 optimization, the trajectory tracking performance and the stability of the closed loop system are analyzed. Sufficient conditions are obtained in terms of linear matrix inequalities (LMI). Simulation results show that the proposed controller is robust with respect to uncertainties on the mechanical parameters that characterize the model and secures global convergence.

Robust observer-based fault-tolerant control for vehicle lateral dynamics

This paper presents online sensor Fault Detection and Isolation (FDI) and the associated Fault-Tolerant Control (FTC) algorithm for a vehicle lateral dynamics represented by the uncertain Takagi-Sugeno (T-S) fuzzy model. The fault-detection scheme is based on a bank of observers method. Using the LMI formulation, the T-S fuzzy model of the vehicle non-linear dynamics is used to design an observer-based output feedback controller. To demonstrate the effectiveness of the proposed strategy, simulation results are given.

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.

On stability and stabilization of singular uncertain Takagi–Sugeno fuzzy systems☆

Abstract This paper deals with the problem of robust stability and robust stabilization for a class of continuous-time singular Takagi–Sugeno fuzzy systems. Sufficient conditions on stability and stabilization are proposed in terms of strict LMI (Linear Matrix Inequality) for uncertain T–S fuzzy models. In order to reduce the conservatism of results developed using quadratic method, an approach based on non-quadratic Lyapunov functions and S-procedure is proposed. Illustrative examples are given to show the effectiveness of the given results.

Comment on “Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties”

In the paper from Shaocheng Tong and Hiong Li [Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties, Fuzzy Sets and Systems (131) (2002) 165-184], a method to design an observer-based robust fuzzy control of uncertain fuzzy models is proposed. However, the results obtained are not correct. This note intends to circumvent these problems by modifying the result proposed in the aforementioned paper.

Fuzzy control for Electric Power Steering System with assist motor current input constraints

Abstract Friction and disturbances of the road are the main sources of nonlinearity in the Electric Power Steering (EPS) System. Consequently, conventional linear controllers design based on a simplified linear model of the EPS system will result in poor dynamic performance or system instability. On the other hand, a brush-type DC motor is more used in EPS control with an input current that is limited in practice. The control laws designed without taking into account the saturation effect may have undesirable consequences on the system stability. In this paper, a Takagi–Sugeno (T−S) fuzzy is used to represent the nonlinear behavior of an EPS system, and stabilization conditions for nonlinear EPS system with both constrained and saturated control input cases are proposed in terms of linear matrix inequalities (LMI). Simulation results show that both the saturated and constrained controls can stabilize the resulting closed-loop EPS system and provide a stable driving in the presence of nonlinear friction, disturbance of the road and actuator saturation.