Ahmed El Hajjaji

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.

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.

Observer-Based Robust

In this paper, a method of robust H∞ reliable control for uncertain Takagi-Sugeno (T-S) fuzzy systems with unavailable states and time-varying delay is developed. In terms of linear-matrix inequalities (LMIs), we derive sufficient conditions for the existence of the fuzzy observer and the reliable fuzzy controller. The single-step LMI conditions, depending on the size of the delay, are proposed for the observer-based H∞ reliable controller design. This overcomes the drawback of two-step LMI approach in literature. Moreover, the designed fuzzy controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation but in the presence of some actuator faults as well. The result is given without the assumption of the rate of change of time-delay function (i.e., |τ̊| <; 1), which makes it applicable to both slow and fast time-varying delayed systems. Without considering reliability, the proposed result is much less conservative than most of the existing results. Finally, several examples are given to show the effectiveness and advantages of our results.

H_{\infty }

This article deals with sufficient conditions of asymptotic stability for discrete two-dimensional (2D) time switching systems represented by a model of Roesser type with state feedback control. This class of systems can correspond to 2D state space or 2D time space switching systems. This work is based on common and multiple Lyapunov functions. The results are presented in LMI form. Two examples are given to illustrate the results.

Reliable Control for Uncertain T–S Fuzzy Systems With State Time Delay

In this paper, we investigate the problem of non-fragile H∞ fuzzy control design for continuous Takagi Sugeno (T-S) fuzzy systems with uncertainties, external disturbance and unmeasurable state variables. For the case of controller and observer gain additive variations, we propose a new solution of the fragility problem by developing the non-fragile design schemes ensuring the asymptotic stability and H∞ performance for the resulting closed loop systems. By considering a fuzzy Lyapunov function and by introducing slack variables, we propose the new sufficient stabilization conditions formulated in LMI constraints which can be easily solved using the convex optimization tools. The effectiveness the proposed results are illustrated through three numerical examples.

Stabilisation of discrete 2D time switching systems by state feedback control

Abstract This paper deals with the problem of stabilization by state feedback control of Takagi–Sugeno (T–S) fuzzy discrete-time systems with multiple fixed delays while imposing positivity in closed-loop. The obtained results are presented under linear programming (LP) form. In particular, the synthesis of state feedback controllers is first solved in terms of Linear programming for the unbounded controls case. This result is then extended to the stabilization problem by nonnegative controls, and stabilization by bounded controls. The stabilization conditions are derived using the single Lyapunov–Krasovskii functional (LKF). An example of a real plant is studied to show the advantages of the design procedure. A comparison between linear programming and LMI approaches is presented.

Non-fragile H∞ output feedback control design for continuous-time fuzzy systems

This article focuses on the problem of robust H ∞ control for uncertain T–S fuzzy systems with time-varying delay. By employing a novel technique, new delay-dependent stabilisation conditions for the existence of a robust H ∞ controller are obtained based on the parallel distributed compensation method. The result obtained is an important contribution as it establishes a new way that can reduce the conservatism without imposing any restrictions and computational efforts at the same time. In this article, all the conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using LMI optimisation techniques. Two numerical examples are given to demonstrate the merits of the approach proposed in this article. Finally, application to control a truck-trailer is also given to demonstrate the effectiveness of the proposed design method.

Stabilization of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays and bounded controls

The H∞ filtering problem for two-dimensional Takagi–Sugeno fuzzy systems described by the Fornasini–Marchesini (FM) model is studied. Attention is focused on the design of an H∞ fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H∞ performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H∞ fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism.

Robust H∞ control for T-S fuzzy systems with time-varying delay

This paper describes a vehicle dynamics fuzzy control design to improve stability and minimize the rollover risk of the vehicle in critical situations. To obtain a robust controller, several aspects that directly affect the behavior of the vehicle have been considered. Nonlinearities of the lateral forces have been considered by using a Takagi-Sugeno (TS) representation, changes in road friction have been taken into account by introducing parameter uncertainties, and, finally, the road bank angle is considered as an unknown input in the used vehicle dynamics model. A TS observer has been proposed and designed with unmeasurable premise variables in order to consider the unavailability of the sideslip angle measurement. The observer and controller gains are simultaneously obtained by solving the proposed linear matrix inequalities constraints. A fishhook test is conducted in a CarSim simulator in order to illustrate the performance of the designed controller.

H ∞ Filtering of Two-Dimensional T-S Fuzzy Systems

This paper deals with the H∞ estimation of both system state and faults for T-S (Takagi-Sugeno) fuzzy model with bounded input disturbances. Based on the descriptor technique, the sensor faults are considered as an auxiliary state variable. Then a descriptor observer for the obtained augmented system is designed and the observer gains are determined in LMI (Linear Matrix Inequalities) formulation. This method has the advantage to estimate the state variables and the sensor faults simultaneously with H∞ approach. Numerical example shows the efficiency of the proposed method.