Distributed Fuzzy Control Design of Nonlinear Hyperbolic PDE Systems With Application to Nonisothermal Plug-Flow Reactor

Fuzzy Robust Tracking Control for Uncertain Nonlinear Time-Delay System

“…u l (t) and u f (t) are designed as (8) and (10), respectively. For the fuzzy model represented by (2) or (3), fuzzy state feedback control u l (t) shares the same IF parts with the following structure.…”

“…This particular structure offers a general framework to represent the nonlinear system which is favorable for system analysis. Fuzzy controllers [2][3][4] were proposed to handle the nonlinear system represented by the fuzzy T-S model. To avoid the effect of the uncertainties, a matching condition is assumed in [5][6][7], and an upper bound on uncertainties is introduced in [8][9][10].…”

A multi-model approach to Saint-Venant equations: A stability study by LMIs

“…The tools for the LMI technique developed in infinite dimensions have not been found by the authors and we try to developed those making a parallel with known techniques. Wang et al (2011) also used an LMI technique for the stability study.…”

“…The use of the multi-model representation for a stability study of systems described by nonlinear PDEs is something new in the literature on such systems, but some researchers like Wang et al (2011) have recently developed a control strategy using Takagi-Sugeno models for nonlinear PDE systems with a stability study. More generally, common approaches are based on a finite dimensional approximation of the nonlinear PDE and adaptive control.…”

Highlighted Aspects From Black Box Fuzzy Modeling For Advanced Control Systems Design

“…The control law is parameterized as a dynamic output feedback that is dependent on the membership functions, and the closed-loop stability is specified by the notion of quadratic boundedness. In (Wang et al, 2011) is considered the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first-order hyperbolic partial differential equations (PDEs), where the control actuators are continuously distributed in space. The goal of this methodology is to develop a fuzzy state-feedback control design methodology for these systems by employing a combination of PDE theory and concepts from Takagi-Sugeno fuzzy control.…”