Simultaneous Linear Control for Non-linear Uncertain Systems Described by Takagi-Sugeno Fuzzy Model

2012 ◽  
Author(s):  
Guo Shuxiang ◽  
Li Youxian
Keyword(s):  
Uncertain Systems ◽  
Fuzzy Model ◽  
Linear Control ◽  
Non Linear ◽  
Takagi Sugeno

scholarly journals Bibo Stabilisation of Continuous–Time Takagi–Sugeno Systems under Persistent Perturbations and Input Saturation

2018 ◽  
Vol 28 (3) ◽  
pp. 457-472 ◽  
Author(s):  
José V. Salcedo ◽  
Miguél Martínez ◽  
Sergio García-Nieto ◽  
Adolfo Hilario
Keyword(s):  
Continuous Time ◽  
Closed Loop ◽  
Input Saturation ◽  
Fuzzy Model ◽  
Maximum Volume ◽  
Ts Fuzzy Model ◽  
Non Linear ◽  
Non Linear System ◽  
Takagi Sugeno ◽  
Fuzzy State

Abstract This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi-Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

Non-Linear Control for Uncertain Systems

1994 ◽  
Vol 208 (4) ◽  
pp. 205-213
Author(s):  
S K Spurgeon
Keyword(s):  
Uncertain Systems ◽  
Linear Models ◽  
State Of The Art ◽  
Linear Control ◽  
Control System Design ◽  
Mathematical Concepts ◽  
Points Of Interest ◽  
Non Linear ◽  
Robust Control System ◽  
Linear Controllers

This paper presents a review of a number of state-of-the-art non-linear control design techniques which may be readily applied to solve practical problems in a robust fashion. It is first shown that non-linear controllers may be designed using straightforward linear models with minimal recourse to abstract mathematical concepts. More involved philosophies for robust control system design of inherently non-linear plants are then briefly described. A straightforward yet rigorous design framework is then presented to implement the philosophy. Tutorial examples are presented throughout the paper in order to illustrate major points of interest.

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