Abstract

This paper presents a new structure of Takagi-Sugeno (T-S) fuzzy controllers, which is called T-S fuzzy region controller or TSFRC for short. The fuzzy region concept is used to partition the plant rules into several fuzzy regions so that only one region is fired at the instant of each input vector being coming. Because each fuzzy region contains several plant rules, the fuzzy region can be regarded as a polytopic uncertain model. Therefore, robust control techniques would be essential for designing the feedback gains of each fuzzy region. To improve the speed of response, the decay rate constraint is imposed when deriving the stability conditions with Lyapunov stability criterion. To design TSFRC with the linear matrix inequality (LMI) solver, all stability conditions are represented in terms of LMIs. Finally, a two-link robot system is used to prove the feasibility and validity of the proposed method.

Issue Section:
Technical Papers
Keywords:
general Takagi-Sugeno fuzzy systems, fuzzy region controller, robust control techniques, linear matrix inequality (LMI) optimization, fuzzy control, robust control, Lyapunov methods, linear matrix inequalities, robots, control system synthesis
Topics:
Control equipment, Design, Robust control, Stability, Linear matrix inequalities
1.
Park
,
Y.
,
Tahk
,
M. J.
, and
Park
,
J.
, 2001, “
Optimal Stabilization of Takagi-Sugeno Fuzzy-Systems With Application to Spacecraft Control
,”
J. Guid. Control Dyn.
0731-5090,
24
(
4
), pp.
767
–
777
.
Crossref
Search ADS
 
2.
Taniguchi
,
T.
,
Tanaka
,
K.
, and
Wang
,
H. O.
, 2000, “
Fuzzy Descriptor Systems and Nonlinear Model-Following Control
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
8
(
4
), pp.
442
–
452
.
Crossref
Search ADS
 
3.
Tuan
,
H. D.
,
Apkarian
,
P.
,
Narikiyo
,
T.
, and
Yamamoto
,
Y.
, 2001, “
Parameterized Linear Matrix Inequality Techniques in Fuzzy Control-System Design
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
9
(
2
), pp.
324
–
332
.
Crossref
Search ADS
 
4.
Tseng
,
C. S.
,
Chen
,
B. S.
, and
Uang
,
H. J.
, 2001, “
Fuzzy Tracking Control Design for Nonlinear Dynamic-Systems Via T-S Fuzzy Model
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
9
(
3
), pp.
381
–
392
.
Crossref
Search ADS
 
5.
Lee
,
K. R.
,
Jeung
,
E. T.
, and
Park
,
H. B.
, 2001, “
Robust Fuzzy H-Infinity Control for Uncertain Nonlinear-Systems Via State-Feedback—An LMI Approach
,”
Fuzzy Sets Syst.
0165-0114,
120
(
1
), pp.
123
–
134
.
6.
Tanaka
,
K.
,
Ikeda
,
T.
, and
Wang
,
H. O.
, 1998, “
Fuzzy Regulators and Fuzzy Observers—Relaxed Stability Conditions and LMI-Based Designs
,”
IEEE Trans. Fuzzy Syst.
1063-6706,
6
(
2
), pp.
250
–
265
.
Crossref
Search ADS
 
7.
Tanaka
,
K.
, and
Wang
,
H. O.
, 2001,
Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
,
Wiley
,
New York
.
Crossref
Search ADS
 
8.
Cao
,
Y. Y.
, and
Frank
,
P. M.
, 2001, “
Stability Analysis and Synthesis of Nonlinear Time-Delay Systems Via Linear Takagi-Sugeno Fuzzy Models
,”
Fuzzy Sets Syst.
0165-0114,
124
(
2
), pp.
213
–
229
.
Crossref
Search ADS
 
9.
Chen
,
B. S.
,
Tsai
,
C. L.
, and
Chen
,
Y. F.
, 2001, “
Mixed H-2/H-Infinity Filtering Design in Multirate Transmultiplexer Systems—LMI Approach
,”
IEEE Trans. Signal Process.
1053-587X,
49
(
11
), pp.
2693
–
2701
.
Crossref
Search ADS
 
10.
Lam
,
H. K.
,
Leung
,
F. H. F.
, and
Tam
,
P. K. S.
, 2002, “
A Linear Matrix Inequality Approach for the Control of Uncertain Fuzzy
,”
IEEE Control Syst. Mag.
0272-1708,
22
(
4
), pp.
20
–
25
.
11.
Hong
,
S. K.
, and
Langari
,
R.
, 2000, “
An LMI-Based H-Infinity Fuzzy Control-System Design With TS Framework
,”
Inf. Sci. (N.Y.)
0020-0255,
123
(
3–4
), pp.
163
–
179
.
12.
Gahinet
,
P.
,
Nemirovski
,
A.
,
Laub
,
A. J.
, and
Chilali
,
M.
, 1995,
LMI Control Toolbox
,
The Math Work Inc.
,
Natick, MA
.
Crossref
Search ADS
 
13.
Wang
,
W. J.
, and
Sun
,
C. S.
, 2002, “
Relaxed Stability Condition for T-S Fuzzy Discrete System
,”
Hawaii
,
1
, pp.
244
–
249
.
14.
Chilali
,
M.
, and
Gahinet
,
P.
, 1996, “
H-Infinity Design With Pole-Placement Constraints—An LMI Approach
,”
IEEE Trans. Autom. Control
0018-9286,
41
(
3
), pp.
358
–
367
.
Crossref
Search ADS
 
15.
Chilali
,
M.
,
Gahinet
,
P.
, and
Apkarian
,
P.
, 1999, “
Robust Pole-Placement in LMI Regions
,”
IEEE Trans. Autom. Control
0018-9286,
44
(
12
), pp.
2257
–
2270
.
Crossref
Search ADS
 
16.
Gahinet
,
P.
,
Apkarian
,
P.
, and
Chilali
,
M.
, 1996, “
Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty
,”
IEEE Trans. Autom. Control
0018-9286,
41
(
3
), pp.
436
–
442
.
Crossref
Search ADS
 
17.
Weinmann
,
A.
, 1992,
Uncertain Models and Robust Control
,
Springer-Verlag
,
Berlin
.
Crossref
Search ADS
 
18.
Angeli
,
D.
, and
Mosca
,
E.
, 2002, “
Lyapunov-Based Switching Supervisory Control of Nonlinear Uncertain Systems
,”
IEEE Trans. Autom. Control
0018-9286,
47
(
3
), pp.
500
–
505
.
Crossref
Search ADS
 
19.
Leonessa
,
A.
,
Haddad
,
W. M.
, and
Chellaboina
,
V. S.
, 2001, “
Nonlinear System Stabilization Via Hierarchical Switching Control
,”
IEEE Trans. Autom. Control
0018-9286,
46
(
1
), pp.
17
–
28
.
Crossref
Search ADS
 
20.
Corradini
,
M. L.
,
Jetto
,
L.
, and
Orlando
,
G.
, 2004, “
Robust Stabilization of Multivariable Uncertain Plants Via Switching Control
,”
IEEE Trans. Autom. Control
0018-9286,
49
(
1
), pp.
107
–
114
.
Crossref
Search ADS
 
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 by American Society of Mechanical Engineers
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