Salim Labiod

Adaptive fuzzy control of a class of MIMO nonlinear systems

This paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time multi-input multi-output nonlinear dynamic systems. Within these schemes, fuzzy systems are employed to approximate the plants unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors. By using a regularized matrix inverse, a stable well-defined adaptive controller is firstly investigated. Then, in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values, a second adaptive controller is proposed. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semi-global stability and asymptotic convergence to zero of tracking errors can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems

This paper presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Based on the implicit function theory, the existence of an ideal controller, that can achieve control objectives, is firstly shown. Since the implicit function theory guarantees only the existence of the ideal controller and does not provide a way for constructing it, a fuzzy system is employed to approximate this unknown ideal control law. The adjustable parameters in the used fuzzy system are updated using a gradient descent adaptation algorithm. This algorithm is designed in order to minimize a quadratic cost function of the error between the unknown ideal implicit controller and the used fuzzy control law. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking error converges to a neighborhood of zero. The effectiveness of the proposed adaptive control scheme is demonstrated through the simulation of a simple nonaffine nonlinear system.

Direct adaptive fuzzy control for a class of MIMO nonlinear systems

This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

Non-quadratic local stabilization for continuous-time Takagi--Sugeno models

This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non-PDC control law is proposed according to the non-quadratic nature of the Lyapunov function. Examples are provided to show the advantages over the quadratic and some non-quadratic approaches.

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.

Tuning fuzzy PD and PI controllers using reinforcement learning.

In this paper, we propose a new auto-tuning fuzzy PD and PI controllers using reinforcement Q-learning (QL) algorithm for SISO (single-input single-output) and TITO (two-input two-output) systems. We first, investigate the design parameters and settings of a typical class of Fuzzy PD (FPD) and Fuzzy PI (FPI) controllers: zero-order Takagi-Sugeno controllers with equidistant triangular membership functions for inputs, equidistant singleton membership functions for output, Larsens implication method, and average sum defuzzification method. Secondly, the analytical structures of these typical fuzzy PD and PI controllers are compared to their classical counterpart PD and PI controllers. Finally, the effectiveness of the proposed method is proven through simulation examples.

Tuning fuzzy PID controllers using ant colony optimization

Ant colony optimization (ACO) is one of the swarm intelligence (SI) techniques. It is a bio-inspired optimization method that has proven its success through various combinatorial optimization problems. This paper proposes an ant colony optimization algorithm for tuning fuzzy PID controllers. First, the design of typical Takagi-Sugeno (TS) fuzzy PID controllers is investigated. The tuning parameters of these controllers have physical meaning which makes its tuning task easier than conventional PID controllers. Simulation examples are provided to illustrate the efficiency of the proposed method.

A stable self-tuning proportional-integral-derivative controller for a class of multi-input multi-output nonlinear systems

This paper proposes a self-tuned proportional-integral-derivative (PID) controller for a class of uncertain continuous-time multi-input multi-output nonlinear dynamic systems. Within this scheme, the PID controller is employed to approximate an unknown ideal controller that can achieve control objectives. The three PID control gains are adjustable parameters and they are updated online with a stable adaptation mechanism designed to minimize the error between the unknown ideal controller and the used PID controller. The proposed approach can be regarded as a simple and effective model-free control because the mathematical model of the system is assumed unknown. The stability analysis of the closed-loop system is performed using a Lyapunov approach. It is proved that all signals in the closed-loop system are uniformly ultimately bounded and that the tracking error can be made to converge to zero in the absence of approximation errors. The effectiveness of the proposed adaptive PID control is demonstrated in simulation.

Adaptive sensor-fault tolerant control for a class of multivariable uncertain nonlinear systems

This paper deals with the active fault tolerant control (AFTC) problem for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems subject to sensor faults and external disturbances. The proposed AFTC method can tolerate three additive (bias, drift and loss of accuracy) and one multiplicative (loss of effectiveness) sensor faults. By employing backstepping technique, a novel adaptive backstepping-based AFTC scheme is developed using the fact that sensor faults and system uncertainties (including external disturbances and unexpected nonlinear functions caused by sensor faults) can be on-line estimated and compensated via robust adaptive schemes. The stability analysis of the closed-loop system is rigorously proven using a Lyapunov approach. The effectiveness of the proposed controller is illustrated by two simulation examples.

H ∞ Fuzzy Control of DC-DC Converters with Input Constraint

This paper proposes a method for designing fuzzy control of DC-DC converters under actuator saturation. Because linear control design methods do not take into account the nonlinearity of the system, a T-S fuzzy model and a controller design approach is used. The designed control not only handles the external disturbance but also the saturation of duty cycle. The input constraint is first transformed into a symmetric saturation which is represented by a polytopic model. Stabilization conditions for the state feedback system of DC-DC converters under actuator saturation are established using the Lyapunov approach. The proposed method has been compared and verified with a simulation example.