Due to the universal approximation capability of Takagi–Sugeno (T–S) fuzzy models for nonlinear dynamics, many control issues have been investigated based on fuzzy control theory. In this paper, a transformation procedure is proposed to convert fuzzy models into linear fractional transformation (LFT) models. Then, T–S fuzzy systems can be regarded as a special case of linear parameter-varying (LPV) systems which proved useful for nonlinear control problems. The newly established connection between T–S fuzzy models and LPV models provides a new perspective of the control problems for T–S fuzzy systems and facilitates the fuzzy control designs. Specifically, an output feedback gain-scheduling control design approach for T–S fuzzy systems is presented to ensure globally asymptotical stability and optimize performance of the closed-loop systems. The control synthesis problem is cast as a convex optimization problem in terms of linear matrix inequalities (LMIs). Two examples have been used to illustrate the efficiency of the proposed method.
Issue Section:
Research Papers
References
1.
Ying
, H.
, 1998
, “Sufficient Conditions on Uniform Approximation of Multivariate Functions by General Takagi-Sugeno Fuzzy Systems With Linear Rule Consequent
,” IEEE Trans. Syst., Man Cybern., Part A: Syst. Hum.
, 28
(4
), pp. 515
–520
.2.
Takagi
, T.
, and Sugeno
, M.
, 1985
, “Fuzzy Identification of Systems and Its Applications to Modeling and Control
,” IEEE Trans. Syst., Man Cybern.
, 15
(1
), pp. 116
–132
.3.
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.
, 6
(2
), pp. 250
–265
.4.
Tanaka
, K.
, and Sugeno
, M.
, 1992
, “Stability Analysis and Design of Fuzzy Control Systems
,” Fuzzy Sets Syst.
, 45
(2
), pp. 135
–156
.5.
Wang
, H. O.
, Tanaka
, K.
, and Griffin
, M. F.
, 1996
, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues
,” IEEE Trans. Fuzzy Syst.
, 4
(1
), pp. 14
–23
.6.
Lam
, H. K.
, and Leung
, F. H.
, 2010
, Stability Analysis of Fuzzy-Model-Based Control Systems: Linear-Matrix-Inequality Approach
, Springer-Verlag
, Berlin
.7.
Lam
, H. K.
, Seneviratne
, L. D.
, and Ban
, X.
, 2012
, “Fuzzy Control of Nonlinear Systems Using Parameter-Dependent Polynomial Fuzzy Model
,” IET Control Theory Appl.
, 6
(11
), pp. 1645
–1653
.8.
Lo
, J. C.
, and Lin
, M. L.
, 2003
, “Robust Nonlinear Control Via Fuzzy Static Output Feedback
,” IEEE Trans. Circuits Syst. I: Regular Pap.
, 50
(11
), pp. 1494
–1502
.9.
Kau
, S. W.
, Lee
, H. J.
, Yang
, C. M.
, Lee
, C. H.
, Hong
, L.
, and Fang
, C. H.
, 2007
, “Robust Fuzzy Static Output Feedback Control of T-S Fuzzy Systems With Parametric Uncertainties
,” Fuzzy Sets Syst.
, 158
(2
), pp. 135
–146
.10.
Qiu
, J.
, Feng
, G.
, and Gao
, H.
, 2010
, “Fuzzy-Model-Based Piecewise Static-Output-Feedback Controller Design for Networked Nonlinear Systems
,” IEEE Trans. Fuzzy Syst.
, 18
(5
), pp. 919
–934
.11.
Chadli
, M.
, and Guerra
, T. M.
, 2012
, “LMI Solution for Robust Static Output Feedback Control of Discrete Takagi-Sugeno Fuzzy Models
,” IEEE Trans. Fuzzy Syst.
, 20
(6
), pp. 1160
–1165
.12.
Lam
, H. K.
, and Li
, H.
, 2013
, “Output-Feedback Tracking Control for Polynomial Fuzzy Systems
,” IEEE Trans. Ind. Electron.
, 60
(12
), pp. 5830
–5840
.13.
Lo
, J. C.
, and Lin
, M. L.
, 2004
, “Observer-Based Robust Control for Fuzzy Systems Using Two-Step Procedure
,” IEEE Trans. Fuzzy Syst.
, 12
(3
), pp. 350
–359
.14.
Tseng
, C. S.
, and Hwang
, C. K.
, 2007
, “Fuzzy Observer-Based Fuzzy Control Design for Nonlinear Systems With Persistent Bounded Disturbances
,” Fuzzy Sets Syst.
, 158
(2
), pp. 164
–179
.15.
Lam
, H. K.
, Li
, H.
, and Liu
, H.
, 2013
, “Stability Analysis and Control Synthesis for a Fuzzy-Observer-Based Controller of Nonlinear Systems: A Fuzzy-Model-Based Control Approach
,” IET Control Theory Appl.
, 7
(5
), pp. 663
–672
.16.
Li
, J.
, Wang
, H. O.
, Niemann
, D.
, and Tanaka
, K.
, 2000
, “Dynamic Parallel Distributed Compensation for Takagi-Sugeno Fuzzy Systems: An LMI Approach
,” Inf. Sci.
, 123
(3–4
), pp. 201
–221
.17.
Han
, Z. X.
, Feng
, G.
, Walcott
, B. L.
, and Ma
, J.
, 2000
, “Dynamic Output Feedback Controller Design for Fuzzy Systems
,” IEEE Trans. Syst., Man, Cybern. Part B, Cybern.
, 30
(1
), pp. 204
–210
.18.
Nguang
, S. K.
, and Shi
, P.
, 2006
, “Robust Output Feedback Control Design for Fuzzy Dynamic Systems With Quadratic Stability Constrains: An LMI Approach
,” Inf. Sci.
, 176
(15
), pp. 2161
–2191
.19.
Yoneyama
, J.
, 2006
, “Robust Control Analysis and Synthesis for Takagi-Sugeno General Uncertain Fuzzy Systems
,” Fuzzy Sets Syst.
, 157
(16
), pp. 2205
–2223
.20.
Guelton
, K.
, Bouarar
, T.
, and Manamanni
, N.
, 2009
, “Robust Dynamic Output Feedback Fuzzy Lyapunov Stabilization of Takagi-Sugeno Systems: A Descriptor Redundancy Approach
,” Fuzzy Sets Syst.
, 160
(19
), pp. 2796
–2811
.21.
Yang
, G. H.
, and Dong
, J.
, 2010
, “Switching Fuzzy Dynamic Output Feedback Control for Nonlinear Systems
,” IEEE Trans. Syst., Man, Cybern. Part B, Cybern.
, 40
(2
), pp. 505
–516
.22.
Tognetti
, E. S.
, Oliveira
, R. C. L. F.
, and Peres
, P. L. D.
, 2012
, “Reduced-Order Dynamic Output Feedback Control of Continuous-Time T-S Fuzzy Systems
,” Fuzzy Sets Syst.
, 207
, pp. 27
–44
.23.
Kim
, E.
, and Lee
, H.
, 2000
, “New Approaches to Relaxed Quadratic Stability Condition of Fuzzy Control Systems
,” IEEE Trans. Fuzzy Syst.
, 8
(5
), pp. 523
–534
.24.
Teixiera
, M. C. M.
, Assuncao
, E.
, and Avellar
, R. G.
, 2003
, “On Relaxed LMI-Based Designs for Fuzzy Regulators and Fuzzy Observers
,” IEEE Trans. Fuzzy Syst.
, 11
(5
), pp. 613
–623
.25.
Tanaka
, K.
, Hori
, T.
, and Wang
, H. O.
, 2003
, “A Multiple Lyapunov Function Approach to Stabilization of Fuzzy Control Systems
,” IEEE Trans. Fuzzy Syst.
, 11
(4
), pp. 582
–589
.26.
Rugh
, W. J.
, and Shamma
, J. S.
, 2000
, “Research on Gain Scheduling
,” Automatica
, 36
(10
), pp. 1401
–1425
.27.
Balas
, G. J.
, Fialho
, I.
, Packard
, A. K.
, Renfrow
, J.
, and Mullaney
, C.
, 1997
, “On the Design of LPV Controllers for the F-14 Aircraft Lateral-Directional Axis During Powered Approach
,” American Control Conference
, pp. 123
–127
.28.
Apkarian
, P.
, and Adams
, R.
, 1998
, “Advanced Gain-Scheduling Techniques for Uncertain Systems
,” IEEE Trans. Control Syst. Technol.
, 6
(1
), pp. 21
–32
.29.
Wu
, F.
, Packard
, A.
, and Balas
, G.
, 2002
, “Systematic Gain-Scheduling Control Design: A Missile Autopilot Example
,” Asian J. Control
, 4
(3
), pp. 341
–347
.30.
Tsourdos
, A.
, Economou
, J. T.
, White
, B. A.
, and Luk
, P. C. K.
, 2003
, “Control Design for a Mobile Robot: A Fuzzy LPV Approach
,” IEEE Conference on Control Applications
, pp. 552
–557
.31.
Huang
, Y.
, Sun
, C.
, Qian
, C.
, Zhang
, R.
, and Zhang
, J.
, 2012
, “Polytopic LPV Gain-Scheduled Control for a Flexible Air-Breathing Hypersonic Vehicle
,” 31st Chinese Control Conference
, pp. 329
–334
.32.
Precup
, R. E.
, Dragos
, C. A.
, Preitl
, S.
, Radac
, M. B.
, and Petriu
, E. M.
, 2012
, “Novel Tensor Product Models for Automatic Transmission System Control
,” IEEE Syst. J.
, 6
(3
), pp. 488
–498
.33.
Hanifzadegan
, M.
, and Nagamune
, R.
, 2014
, “Smooth Switching LPV Controller Design for LPV Systems
,” Automatica
, 50
(5
), pp. 1481
–1488
.34.
Packard
, A. K.
, 1994
, “Gain Scheduling Via Linear Fractional Transformations
,” Syst. Control Lett.
, 22
(2
), pp. 79
–92
.35.
Apkarian
, P.
, and Gahinet
, P.
, 1995
, “A Convex Characterization of Gain-Scheduled Controllers
,” IEEE Trans. Autom. Control
, 40
(5
), pp. 853
–864
.36.
Chilali
, M.
, and Gahinet
, P.
, 1996
, “ Design With Pole Placement Constraints: An LMI Approach
,” IEEE Trans. Autom. Control
, 41
(3
), pp. 358
–367
.Copyright © 2016 by ASME
You do not currently have access to this content.
