Kevin Guelton

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.

New controllers and new designs for continuous-time Takagi-Sugeno models

This work presents a new non-PDC controller design based on different Lyapunov functions for continuous-time Takagi-Sugeno models. Based on this new control law and on Finslers lemma a new way to derive LMI constraints problems is presented. Both quadratic and non quadratic Lyapunov functions are under consideration. Some examples show the capability of outperforming existing results without increasing significantly the LMI problems.

Static Output Feedback controller design for Takagi-Sugeno systems - a Fuzzy Lyapunov LMI approach

This paper deals with Takagi-Sugeno (T-S) systems stabilization based on a Static Output Feedback (SOF) non-PDC control law. To investigate SOF stabilization, the closed loop dynamics is written using a descriptor redundancy formulation. This approach allows avoiding appearance of crossing terms between the controllers and the T-S systems matrices. Thus, based on a Fuzzy Lyapunov candidate Function (FLF), a LMI based design methodology is provided. Then, a H-infinity criterion is considered to attenuate external disturbances. Finally, an academic example illustrates the efficiency of the proposed approach.

Robust non-quadratic static output feedback controller design for Takagi-Sugeno systems using descriptor redundancy

This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi-Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controllers and the TS systems input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions do not require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology.

Actuator and sensor fault detection and isolation of an actuated seat via nonlinear multi-observers

In this paper, a model-based approach to detect and to isolate sensors and actuators faults using nonlinear sliding mode observers is proposed for an actuated seat. The goal is to ensure the comfort and the security of the users in simulators applications. The principle is to reconstruct the state vector of the system by sliding mode observers and to compare the estimated outputs with those measured as residuals. In this work, a multi-observers technique is used. It consists of designing multiple observers such that each observer must be robust to noises and to other uncertainties but sensitive to each actuator or sensor fault. Simulation results are given to show the effectiveness of the approach.

LMI Stability Conditions for Takagi-Sugeno Uncertain Descriptors

In this paper, stability conditions for a wide class of Takagi-Sugeno uncertain descriptors are proposed. These are based on a quadratic Lyapunov candidate function. In order to solve the stability conditions with classical convex optimization algorithms, matrices transformations have been used to write these conditions in term of linear matrix inequality (LMI). A designed example illustrates the efficiency of the proposed approach.

Stabilization of uncertain Takagi-Sugeno descriptors: A fuzzy Lyapunov approach

This paper presents stability conditions for Takagi-Sugeno (T-S) uncertain descriptors. These are based on a fuzzy Lyapunov approach and a non-PDC (parallel distributed compensation) control scheme. To design the fuzzy controller, the stability conditions are derived into LMIs. Moreover, in order to reduce once more the conservatism of the proposed stability conditions, a relaxation scheme, allowing rewriting the triple summation structure, is introduced for T-S descriptors. A designed example illustrates the efficiency of the proposed approaches.

Modelling and simulation of two-link robot manipulators based on Takagi Sugeno fuzzy descriptor systems

This paper presents the first steps towards a robust model-based controller design for two-link manipulators using a Takagi Sugeno fuzzy descriptor form. Due to the circumstances that this form is more similar to a given original nonlinear equation as a Takagi Sugeno fuzzy state-space system, it allows to reduce the conservatism of the controller design by using common matrix structures. The model-based control law here is equivalent to the well-known parallel distributed compensation scheme. The challenge of the investigated modelling and control problem in this case is the highly nonlinear dynamics of the dual-actuator drive powered by air-pressure that interacts with the dynamics of the robot manipulator.

LMI BASED H∞ CONTROLLER DESIGN FOR UNCERTAIN TAKAGI-SUGENO DESCRIPTORS SUBJECT TO EXTERNAL DISTURBANCES

Abstract This paper deals with the design of an H ∞ fuzzy controller for uncertain T-S fuzzy descriptor with external disturbances. The control scheme is based on the modified PDC control law and an H ∞ criterion to attenuate external disturbances. Stability conditions are obtained via a quadratic Lyapunov function and are given in terms of LMI. To illustrate the efficiency of the proposed approach, a design example is provided with the simulation of a planar two degrees of freedom robot.

A SOS based alternative to LMI approaches for non-quadratic stabilization of continuous-time Takagi-Sugeno fuzzy systems

Nowadays, when dealing with non-quadratic controllers design for continuous-time Takagi-Sugeno (TS) models, LMIs-based successive conditions become more and more complex for a conservatism reduction that is sometime questionable. Therefore, in this paper it is assumed that it should be interesting to explore what can be done, else than LMIs, in the non-quadratic framework. Indeed, in most of the cases, non-quadratic LMIs suffer from the requirement of unknown parameters or lead to local stability analysis. Hence, the aim of this paper is to show, at a first attempt, that the Sum-Of-Squares formalism is suitable to design non-PDC controllers which stabilizing TS models on their whole definition set. However, it is pointed-out that the SOS formalism requires a restrictive modeling assumption, understood as a drawback but opening some possible further prospects.