Abstract
The stabilization problem is considered in this study for a neural-network (NN) linearly interconnected system that consists of a number of NN models. First, a linear difference inclusion (LDI) state-space representation is established for the dynamics of each NN model. Then, based on the LDI state-space representation, a stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of closed-loop NN linearly interconnected systems. Subsequently, according to this criterion and the decentralized control scheme, a set of Takagi-Sugeno (T-S) fuzzy controllers is synthesized to stabilize the NN linearly interconnected system. Finally, a numerical example with simulations is given to demonstrate the concepts discussed throughout this paper.
Issue Section:
Technical Briefs
1.
Tzafestas
, S. G.
, and Watanabe
, K.
, 1992, Stochastic Large-Scale Engineering Systems
, Marcel Dekker
, New York
.2.
Bennett
, W. H.
, and Baras
, J. S.
, 1982, “Design Methods for Decentralized Control of Large-Scale Systems Based on Block Diagonal Dominance
,” IEEE Control Syst. Mag.
0272-1708, 2
(4
), pp. 50
–50
.3.
Ohta
, Y.
, Šiljak
, D. D.
, and Matsumoto
, T.
, 1986, “Decentralized Control Using Quasi-Block Diagonal Dominance of Transfer Function Matrices
,” IEEE Trans. Autom. Control
0018-9286, 31
, pp. 420
–430
.4.
Edmunds
, J. M.
, 1998, “Input and Output Scaling and Reordering for Diagonal Dominance and Block Diagonal Dominance
,” IEE Proc.: Control Theory Appl.
1350-2379, 145
, pp. 523
–530
.5.
Labibi
, B.
, Lohmann
, B.
, Sedigh
, A. K.
, and Maralani
, P. J.
, 2003, “Decentralized Stabilization of Large-Scale Systems Via State-Feedback and Using Descriptor Systems
,” IEEE Trans. Syst. Man Cybern., Part A. Syst. Humans
1083-4427, 33
, pp. 771
–776
.6.
Wang
, W.-J.
, and Luoh
, L.
, 2004, “Stability and Stabilization of Fuzzy Large-Scale Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 12
, pp. 309
–315
.7.
Tobi
, T.
et al., 1991, “A Practical Application of Fuzzy Control for an Air Conditioning System
,” Int. J. Approx. Reason.
0888-613X, 5
, pp. 331
–348
.8.
Eaton
, J. W.
, and Rawlings
, J. B.
, 1992, “Model-Predictive Control of Chemical Processes
,” Chem. Eng. Sci.
0009-2509, 47
, pp. 705
–720
.9.
Wang
, S.-Y.
, Hong
, C.-M.
, Liu
, C.-C.
, and Yang
, W.-T.
, 1996, “Design of a Static Reactive Power Compensator Using Fuzzy Sliding Mode Control
,” Int. J. Control
0020-7179, 63
, pp. 393
–413
.10.
Jin
, Y.
, 1998, “Decentralized Adaptive Fuzzy Control of Robot Manipulators
,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
1083-4419, 28
, pp. 47
–57
.11.
Aldawod
, M.
, Samali
, B.
, Naghdy
, F.
, and Kwok
, K. C. S.
, 2001, “Active Control of Along Wind Response of Tall Building Using a Fuzzy Controller
,” Polym. Polym. Compos.
0967-3911, 23
, pp. 1512
–1522
.12.
Hwang
, C.-L.
, and Kuo
, C.-Y.
, 2001, “A Stable Adaptive Fuzzy Sliding-Mode Control for Affine Nonlinear Systems with Application to Four-Bar Linkage Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 9
, pp. 238
–251
.13.
Mesina
, O. S.
, and Langari
, R.
, 2001, “A Neuro-Fuzzy System for Tool Condition Monitoring in Metal Cutting
,” ASME J. Manuf. Sci. Eng.
1087-1357, 123
, pp. 312
–318
.14.
Tanaka
, K.
, and Sugeno
, M.
, 1992, “Stability Analysis and Design of Fuzzy Control System
,” Fuzzy Sets Syst.
0165-0114, 45
, pp. 135
–156
.15.
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.
1063-6706, 4
, pp. 14
–23
.16.
Feng
, G.
, Cao
, S. G.
, Rees
, N. W.
, and Chak
, C. K.
, 1997, “Design of Fuzzy Control Systems with Guaranteed Stability
,” Fuzzy Sets Syst.
0165-0114, 85
, pp. 1
–10
.17.
Ma
, X.-J.
, Sun
, Z.-O.
, and He
, Y.-Y.
, 1998, “Analysis and Design of Fuzzy Controller and Fuzzy Observer
,” IEEE Trans. Fuzzy Syst.
1063-6706, 6
, pp. 41
–51
.18.
Wang
, W.-J.
, and Lin
, H.-R.
, 1999, “Fuzzy Control Design for the Trajectory Tracking on Uncertain Nonlinear Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 7
, pp. 53
–62
.19.
Chen
, B.-S.
, Tseng
, C.-S.
, and Uang
, H. J.
, 1999, “Robustness Design of Nonlinear Dynamic Systems Via Fuzzy Linear Control
,” IEEE Trans. Fuzzy Syst.
1063-6706, 7
, pp. 571
–585
.20.
Chen
, B.-S.
, Lee
, B.-K.
, and Guo
, L.-B.
, 2003, “Optimal Tracking Design for Stochastic Fuzzy Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 11
, pp. 1
–19
.21.
Cao
, S. G.
, Rees
, N. W.
, and Feng
, G.
, 1996, “Quadratic Stability Analysis and Design of Continuous-Time Fuzzy Control Systems
,” Int. J. Syst. Sci.
0020-7721, 27
, pp. 193
–203
.22.
Cao
, S. G.
, Rees
, N. W.
, and Feng
, G.
, 1996, “Stability Analysis and Design for a Class of Continous-Time Fuzzy Control Systems
,” Int. J. Control
0020-7179, 64
, pp. 1069
–1087
.23.
Cao
, S. G.
, Rees
, N. W.
, and Feng
, G.
, 1998, “Lyapunov-Like Stability Theorems for Continuous-Time Fuzzy Control Systems
,” Int. J. Control
0020-7179, 69
, pp. 49
–64
.24.
Yen
, J.
, and Langari
, R.
, 1998, Fuzzy Logic: Intelligence, Control, and Information
, Prentice Hall
, Englewood Cliffs, NJ
.25.
Akar
, M.
, and Özgüner
, Ü.
, 1999, “Decentralized Parallel Distributed Compensator Design for Takagi-Sugeno Fuzzy Systems
,” Proceedings of the IEEE Conference on Decision and Control
, Vol. 5
, pp. 4834
–4839
.26.
Akar
, M.
, and Özgüner
, Ü.
, 1999, “Stability and Stabilization of Takagi-Sugeno Fuzzy Systems
,” Proceedings of the IEEE Conference on Decision and Control
, Vol. 5
, pp. 4840
–4845
.27.
Akar
, M.
, and Özgüner
, Ü.
, 2000, “Decentralized Techniques for the Analysis and Control of Takagi-Sugeno Fuzzy Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 3
, pp. 691
–704
.28.
Hong
, S.-K.
, and Langari
, R.
, 2000, “An LMI-Based H∞ Fuzzy Control System Design with TS Framework
,” Inf. Sci. (N.Y.)
0020-0255, 123
, pp. 163
–179
.29.
Tanaka
, K.
, 1995, “Stability and Stabilization of Fuzzy-Neural-Linear Control Systems
,” IEEE Trans. Fuzzy Syst.
1063-6706, 3
, pp. 438
–447
.30.
Tanaka
, K.
, 1996, “An Approach to Stability Criteria of Neural-Network Control Systems
,” IEEE Trans. Neural Netw.
1045-9227, 7
, pp. 629
–643
.31.
Limanond
, S.
, and Si
, J.
, 1998, “Neural-Network-Based Control Design: An LMI Approach
,” IEEE Trans. Neural Netw.
1045-9227, 9
, pp. 1422
–1429
.32.
Si
, J.
, and Michel
, A. N.
, 1994, “Analysis and Synthesis of a Class of Discrete-Time Neural Networks with Nonlinear Interconnections
,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl.
1057-7122, 41
, pp. 52
–58
.33.
Si
, J.
, and Michel
, A. N.
, 1995, “Analysis and Synthesis of a Class of Discrete-Time Neural Networks with Multilevel Threshold Neurons
,” IEEE Trans. Neural Netw.
1045-9227, 6
, pp. 105
–116
.34.
Boyd
, S.
, El Ghaoui
, L.
, Feron
, E.
, and Balakrishnan
, V.
, 1994, Linear Matrix Inequalities in System and Control Theory
, SIAM
, Philadelphia, PA
.35.
Wang
, W.-J.
, and Cheng
, C.-F.
, 1992, “Stabilizing Controller and Observer Synthesis for Uncertain Large-Scale Systems by the Riccati Equation Approach
,” IEE Proc.-D: Control Theory Appl.
0143-7054, 139
, pp. 72
–78
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
