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T–S fuzzy BIBO stabilisation of non-linear systems under persistent perturbations using fuzzy Lyapunov functions and non-PDC control laws

Salcedo José V., Martínez Miguel, García-Nieto Sergio, Hilario Adolfo

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 3

529--550

This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi–Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum ⋆-norm (upper bound of the 1-norm) for the T–S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.

Nonlinear actuator fault estimation observer: an inverse system approach via a T-S fuzzy model

Xu D., Jiang B., Shi P.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 1

183-196

Based on a Takagi-Sugeno (T-S) fuzzy model and an inverse system method, this paper deals with the problem of actuator fault estimation for a class of nonlinear dynamic systems. Two different estimation strategies are developed. Firstly, T-S fuzzy models are used to describe nonlinear dynamic systems with an actuator fault. Then, a robust sliding mode observer is designed based on a T-S fuzzy model, and an inverse system method is used to estimate the actuator fault. Next, the second fault estimation strategy is developed. Compared with some existing techniques, such as adaptive and sliding mode methods, the one presented in this paper is easier to be implemented in practice. Finally, two numerical examples are given to demonstrate the efficiency of the proposed techniques.

A novel fuzzy c-regression model algorithm using a new error measure and particle swarm optimization

Soltani M., Chaari A., Ben Hmida F.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 3

617-628

This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.