Takagi–Sugeno fuzzy‐model‐based event‐triggered point control for semilinear partial differential equation systems using collocated pointwise measurements

Abstract

This paper addresses event‐triggered point control design for semilinear partial differential equation systems by using pointwise measurements. First, the nonlinear terms existing in the plant are approximated by Takagi–Sugeno fuzzy model, based on which a novel fuzzy controller is constructed. The main novelties of the control strategy are summarized as follows: (1) The one‐dimensional space is divided into L parts, and only a few points need to measure. (2) Event‐triggered communication scheme is introduced to save the limited transmission channel. (3) Pointwise control is considered to reduce the control cost via utilizing limited actuators. Second, the conditions that guarantee the stability of the closed‐loop system are established by using Lyapunov direct method and some inequality techniques including Wirtinger's and Halanay's inequalities, and the controller gains can be obtained via solving linear matrix inequalities. Third, three simulation examples are provided to verify the effectiveness and superiority of the proposed approach.

Nonuniform piecewise membership function approximation methods based robust tracking control design of T‐S fuzzy systems

“…For system (6), the operation region of z can be separated into q subregions, where q = ∏ p i=1 q i , q i is the uniformly piecewise number on each z i . A region Λ k is formed by the set {z|z ij i min ≤ z ij i ≤ z ij i max }, j i = 1, … , q i and k = 1, … , q, which can be seen as a polyhedron.…”

“…Through a T‐S fuzzy system (formed by sublinear systems and membership functions), nonlinear systems control problems 1,2 in modern industry can be suitably addressed by mature linear control theories 3 . By this effective approach, many nonlinear control problems are satisfactorily solved 4‐7 …”

“…3 By this effective approach, many nonlinear control problems are satisfactorily solved. [4][5][6][7] Tracking control is a kind of meaningful task in real world engineering systems. Due to the unknown external disturbance, the tracking control performance is hard to achieve.…”

Takagi–Sugeno Fuzzy Modeling and Control for Effective Robotic Manipulator Motion

“…This proposed controller showed the high efficiency of avoiding chattering within very accurate tracking. In [15], the nonlinear parts in the dynamic system equation are identified by using T-SFM model. Next, using the obtained model from the T-SFM technique, a new controller is designed depending on estimation principle, i.e., not whole measurements.…”

A switched system approach to exponential filtering design for Takagi–Sugeno fuzzy systems with sampled‐data measurements subject to packet dropouts

“…One of their advantages is that any smooth nonlinear functions can be approximated by T‐S fuzzy models to any degree of accuracy in any convex compact set 3‐6 . Another advantage of T‐S fuzzy models is that they make the investigation of complex nonlinear systems enjoy the well‐developed theory for linear systems 7 . Thanks to their advantages and effectiveness, T‐S fuzzy‐model‐based control systems have drawn a great deal of attention and many elegant results have been reported during the past few decades 8‐12 …”