A. El Hajjaji

Improved fuzzy sliding mode control for a class of MIMO nonlinear uncertain and perturbed systems

In this paper, a stable adaptive fuzzy sliding mode based tracking control is developed for a class of nonlinear MIMO systems that are represented by input output models involving system uncertainties and external disturbances. The main contribution of the proposed method is that the structure of the controller system is partially unknown and does not require the bounds of uncertainties and disturbance to be known. First, a fuzzy logic system is designed to estimate the unknown function. Secondly, in order to eliminate the chattering phenomenon brought by the conventional variable structure control, the signum function is replaced by an adaptive Proportional Derivative (PD) term in the proposed approach. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis, so that convergence to zero of tracking errors and boudedness of all signals in the closed-loop system can be guaranteed. Finally, a mass-spring-damper system is simulated to demonstrate the validity and the effectiveness of the proposed controller.

Observer based (Q,V,R)-α-dissipative control for TS fuzzy descriptor systems with time delay

Abstract This paper is concerned with the design of ( Q , V , R ) - α - dissipative control for continuous TS fuzzy descriptor systems with unmeasurable states and time-varying delay. Our attention is focused on the design of the fuzzy controller and the fuzzy observer such that the closed loop fuzzy descriptor system with time delay is not only regular, impulse-free and stable but also ( Q , V , R ) - α - dissipative . By using the matrix decoupling technique, new delay dependent stabilization conditions are presented in terms of Linear Matrix Inequalities (LMI). As a particular case, observer-based H ∞ control is deduced from the proposed observer-based dissipative control result. Finally, a numerical example is given to demonstrate the effectiveness of our results.

Fuzzy control of a mobile robot: a new approach

This paper presents a new approach to design a fuzzy controller for backing up a mobile robot. After making the dynamics of the mobile robot interpolated by two linear systems, a general analysis and design method are proposed to stabilize it with two fuzzy rules. The method is based on converting the stability analysis of a fuzzy control system to the stability analysis of an overvaluing system for the mobile robot. A sufficient condition based on the use of the comparison system is deduced to guarantee the stability of the mobile robot. To highlight the performance of the new proposed technique, simulation results are presented.

Road curvature estimation for vehicle lane departure detection using a robust Takagi–Sugeno fuzzy observer

In this paper, a lane departure detection method is studied and evaluated via a professional vehicle dynamics software. Based on a robust fuzzy observer designed with unmeasurable premise variables with unknown inputs, the road curvature is estimated and compared with the vehicle trajectory curvature. The difference between the two curvatures is used by the proposed algorithm as the first driving risk indicator. To reduce false alarms and take into account the driver corrections, a second driving risk indicator is considered, which is based on the steering dynamics, and it gives the time to the lane keeping. The used nonlinear model deduced from the vehicle lateral dynamics and a vision system is represented by an uncertain Takagi–Sugeno fuzzy model. Taking into account the unmeasured variables, an unknown input fuzzy observer is then proposed. Synthesis conditions of the proposed fuzzy observer are formulated in terms of linear matrix inequalities using Lyapunov method. The proposed approach is evaluated under different driving scenarios using a software simulator. Simulation results show good efficiency of the proposed method.

Observer-based robust fuzzy control for vehicle lateral dynamics

In this paper, the robust fuzzy control for four wheels steering (4WS) vehicle dynamics is studied via a Takagi-Sugeno (T-S) uncertain fuzzy model when the road adhesion conditions change and the sideslip angle is unavailable for measurement. After giving the nonlinear model of the vehicle, its representation by a T-S uncertain fuzzy model is discussed. Next, based on the uncertain fuzzy model of the 4WS Vehicle a fuzzy controller and a fuzzy observer are developed. The closed loop stability conditions of a vehicle with the fuzzy controller and the observer are parameterized in terms of linear matrix inequality (LMI) problem which can be solved very efficiently using the convex optimization techniques. The numerical simulation of the vehicle handling with and without the use of the developed observer and controller has been carried out. The simulation results obtained indicate that considerable improvements in the vehicle handling can be achieved whenever the vehicle is governed by the proposed fuzzy observer and fuzzy controller

Observer-based robust control of uncertain fuzzy dynamic systems with pole placement constraints: an LMI approach

This paper investigates both analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions involving observer-based fuzzy control. The class of systems considered here is the continuous Takagi-Sugeno (T-S) fuzzy model with parametric structured uncertainties and unavailable state variables. Sufficient global stability conditions are established which make it possible to robustly assign the closed-loop poles of the augmented system containing both the fuzzy controller and observer in the left half complex plane and also to guarantee control performances by imposing a pole placement. Because of uncertainties, the separation property is not applicable to design the fuzzy controller and observer separately. The idea of the proposed approach is to assign both state and estimation error poles to a desired LMI region and to use the Hinfin technique in order to guarantee that the estimation error converges faster to the equilibrium point zero. An example is given to illustrate the effectiveness of the proposed approach

One-Step procedure for robust output h8 fuzzy control

This paper addresses robust observer based Hinfin control problem for Takagi-Sugeno fuzzy systems with time-varying norm bounded uncertainties. Sufficient relaxed conditions for synthesis of a fuzzy observer and a fuzzy controller for T-S fuzzy systems are derived in terms of a set of linear matrix inequalities (LMIs). In comparison with the existing techniques in literature, the proposed approach considerably simplifies the design procedure and gives in only one step the controller and the observer gains. The observer and controller designed are capable to reject the disturbance assumed known but norm bounded. In order to highlight the performance of the proposed control algorithm, numerical simulations are performed.

Lateral vehicle velocity estimation using fuzzy sliding mode observer

This paper presents a robust method for estimation the lateral velocity of vehicle. The proposed observer describes a simple structure that contains a sliding mode term which turns out to be robust against output noises and parameters variations as well as sustained disturbances The given nonlinear model of the vehicle is then represented by an uncertain Takagi-Sugeno fuzzy model when the road adhesion conditions change and the sideslip angle is unavailable for measurement. After giving the nonlinear model of the vehicle, its representation by a T-S uncertain fuzzy model is discussed. Stability conditions of such observers are expressed in terms of linear matrix inequalities (LMI). To illustrate the effectiveness of the proposed design observer, a numerical simulation is given.

Vehicle dynamic estimation with road bank angle consideration for rollover detection: theoretical and experimental studies

This article describes a method of vehicle dynamics estimation for impending rollover detection. This method is evaluated via a professional vehicle dynamics software and then through experimental results using a real test vehicle equipped with an inertial measurement unit. The vehicle dynamic states are estimated in the presence of the road bank angle (as a disturbance in the vehicle model) using a robust observer. The estimated roll angle and roll rate are used to compute the rollover index which is based on the prediction of the lateral load transfer. In order to anticipate the rollover detection, a new method is proposed in order to compute the time-to-rollover using the load transfer ratio. The used nonlinear model is deduced from the vehicle lateral dynamics and is represented by a Takagi–Sugeno (TS) fuzzy model. This representation is used in order to take into account the nonlinearities of lateral cornering forces. The proposed TS observer is designed with unmeasurable premise variables in order to consider the non-availability of the slip angles measurement. Simulation results show that the proposed observer and rollover detection method exhibit good efficiency.

Four-Wheel Steering Vehicle Control using Takagi-Sugeno Fuzzy Models

This paper deals with the problem of vehicle active control. The focus is to improve the vehicle stability and handling. Vehicle dynamics is described by a 10-DOF (degree of freedom) model which include lateral, longitudinal, yaw and roll dynamics. Parametric variations (due to the variation of road conditions) and also, a variation of vehicle velocity are taken into account in the controller synthesis. The nonlinear vehicle model is approximated by a Takagi-Sugeno (T-S) fuzzy model with structured parametric uncertainties. State variables are not always available. Thus, fuzzy observer-based algorithm will be proposed to ensure control with performance specifications. Robust pole placement LMI (linear matrix inequalities) conditions are obtained using Lyapunov and Hinfin approach, which ensure desired performances of the closed loop system.