|
|
Non-fragile control of fuzzy affine dynamic systems via piecewise Lyapunov functions |
Shasha FU, Jianbin QIU( ), Wenqiang JI |
Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin 150001, China |
|
|
Abstract This paper addresses the robust ℋ∞ static output feedback (SOF) controller design problem for a class of uncertain fuzzy affine systems that are robust against both the plant parameter perturbations and controller gain variations. More specifically, the purpose is to synthesize a non-fragile piecewise affine SOF controller guaranteeing the stability of the resulting closed-loop fuzzy affine dynamic system with certainℋ∞ performance index. Based on piecewise quadratic Lyapunov functions and applying some convexification procedures, two different approaches are proposed to solve the robust and non-fragile piecewise affine SOF controller synthesis problem. It is shown that the piecewise affine controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, simulation examples are given to illustrate the effectiveness of the proposed methods.
|
Keywords
fuzzy affine systems
non-fragile
robust output feedback control
|
Corresponding Author(s):
Jianbin QIU
|
Just Accepted Date: 21 July 2016
Online First Date: 31 October 2016
Issue Date: 07 December 2017
|
|
1 |
SalaA, GuerraT M, BabŭskaR . Perspectives of fuzzy systems and control. Fuzzy Sets and Systems, 2005, 156(3): 432–444
https://doi.org/10.1016/j.fss.2005.05.041
|
2 |
FengG. A survey on analysis and design of model-based fuzzy control systems. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 676–697
https://doi.org/10.1109/TFUZZ.2006.883415
|
3 |
TakagiT, SugenoM. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man and Cybernetics, 1985, SMC-15(1): 116–132
https://doi.org/10.1109/TSMC.1985.6313399
|
4 |
TanakaK, WangH O. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley, 2001
https://doi.org/10.1002/0471224596
|
5 |
TeixeiraM C M, Żak S H. Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE Transactions on Fuzzy Systems, 1999, 7(2): 133–142
https://doi.org/10.1109/91.755395
|
6 |
GaoH, ChenT. Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Transactions on Fuzzy Systems, 2007, 15(5): 972–983
https://doi.org/10.1109/TFUZZ.2006.890660
|
7 |
ZhangC, FengG, GaoH, Qiu J. ℋ∞ filtering for nonlinear discretetime systems subject to quantization and packet dropouts. IEEE Transactions on Fuzzy Systems, 2011, 19(2): 353–365
https://doi.org/10.1109/TFUZZ.2010.2098880
|
8 |
LiuM, CaoX, ShiP. Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults. IEEE Transactions on Fuzzy Systems, 2013, 21(5): 789–799
https://doi.org/10.1109/TFUZZ.2012.2224872
|
9 |
QiuJ, GaoH, DingS X. Recent advances on fuzzy-model-based nonlinear networked control systems: a survey. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1207–1217
https://doi.org/10.1109/TIE.2015.2504351
|
10 |
LiL, DingS X, QiuJ, Yang Y. Real-time fault detection approach for nonlinear systems and its asynchronous T-S fuzzy observer-based implementation. IEEE Transactions on Cybernetics, doi: 10.1109/TCYB.2015.2513438
https://doi.org/10.1109/TCYB.2015.2513438
|
11 |
JohanssonM, Rantzer A, ÅrzénK E. Piecewise quadratic stability of fuzzy systems. IEEE Transaction on Fuzzy Systems, 1999, 7(6): 713–722
https://doi.org/10.1109/91.811241
|
12 |
FengG, ChenC L, SunD, Zhu Y. ℋ∞ controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities. IEEE Transactions on Fuzzy Systems, 2005, 13(1): 94–103
https://doi.org/10.1109/TFUZZ.2004.839662
|
13 |
QiuJ, FengG, GaoH. Observer-based piecewise affine output feedback controller synthesis of continuous-time T-S fuzzy affine dynamic systems using quantized measurements. IEEE Transactions on Fuzzy Systems, 2012, 20(6): 1046–1062
https://doi.org/10.1109/TFUZZ.2012.2191790
|
14 |
FuS, WangM, QiuJ, He Y. T-S fuzzy affine model based nonsynchronized state estimation for nonlinear Itô stochastic systems. Neurocomputing, 2015, 167: 424–433
https://doi.org/10.1016/j.neucom.2015.04.052
|
15 |
LiL, DingS X, QiuJ, Yang Y, ZhangY . Weighted fuzzy observerbased fault detection approach for discrete-time nonlinear systems via piecewise-fuzzy Lyapunov functions. IEEE Transactions on Fuzzy Systems, doi: 10.1109/TFUZZ.2016.2514371
https://doi.org/10.1109/TFUZZ.2016.2514371
|
16 |
ZhouK, DoyleJ C, GloverK. Robust Optimal Control, Englewood Cliffs, NJ: Prentice Hall, 2001
|
17 |
ZhangC, FengG, QiuJ, Shen Y. Control synthesis for a class of linear network-based systems with communication constraints. IEEE Transactions on Industrial Electronics, 2013, 60(8): 3339–3348
|
18 |
WeiY, QiuJ, KarimiH R, Wang M. ℋ∞ model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information. International Journal of Systems Science, 2014, 45(7): 1496–1507
https://doi.org/10.1080/00207721.2013.837545
|
19 |
QiuJ, WeiY, KarimiH R. New approach to delay-dependent ℋ∞ control for continuous-time Markovian jump systems with time-varying delay and deficient transition descriptions. Journal of The Franklin Institute, 2015, 352(1): 189–215
https://doi.org/10.1016/j.jfranklin.2014.10.022
|
20 |
WangT, GaoH, QiuJ. A combined adaptive neural network and nonlinear model predictive control for multirate networked industrial process control. IEEE Transactions on Neural Networks and Learning Sys tems, 2016, 27(2): 416–425
https://doi.org/10.1109/TNNLS.2015.2411671
|
21 |
KeelL H, Bhattacharyya S P. Robust, fragile, or optimal? IEEE Transactions on Automatic Control, 1997, 42(8): 1098–1105
https://doi.org/10.1109/9.618239
|
22 |
DuH, LamJ, SzeK Y. Design of non-fragile ℋ∞ controller for active vehicle suspensions. Journal of Vibration and Control, 2005, 11(2): 225–243
https://doi.org/10.1177/1077546305049392
|
23 |
ZhangB, ZhouS, LiT. A new approach to robust and non-fragile ℋ∞ control for uncertain fuzzy systems. Information Sciences, 2007, 177(22): 5118–5133
https://doi.org/10.1016/j.ins.2007.05.004
|
24 |
ChenJ D, YangC D, LienC H, Horng J H. New delay-dependent nonfragile ℋ∞ observer-based control for continuous time-delay systems. Information Sciences, 2008, 178(24): 4699–4706
https://doi.org/10.1016/j.ins.2008.08.009
|
25 |
FanY, LiuL, FengG, Wang Y. Self-triggered consensus for multiagent systems with Zeno-free triggers. IEEE Transactions on Automatic Control, 2015, 60(10): 2779–2784
https://doi.org/10.1109/TAC.2015.2405294
|
26 |
MahmoudM S, Almutairi N B. Resilient decentralized stabilization of interconnected time-delay systems with polytopic uncertainties. International Journal of Robust and Nonlinear Control, 2011, 21(4): 355–372
https://doi.org/10.1002/rnc.1594
|
27 |
DadkhahN, Rodrigues L. Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach. IET Control Theory & Application, 2014, 8(8): 626–632
https://doi.org/10.1049/iet-cta.2013.0202
|
28 |
El GhaouiL, OustryF, AitRamiM. A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 1997, 42(8): 1171–1176
https://doi.org/10.1109/9.618250
|
29 |
QiuJ, FengG, GaoH. Static-output-feedback control of continuoustime T-S fuzzy affine systems via piecewise Lyapunov functions. IEEE Transactions on Fuzzy Systems, 2013, 21(2): 245–261
https://doi.org/10.1109/TFUZZ.2012.2210555
|
30 |
KchaouM, El Hajjaji A, ToumiA . Non-fragile ℋ∞ output feedback control design for continuous-time fuzzy systems. ISA Transactions, 2015, 54: 3–14
https://doi.org/10.1016/j.isatra.2014.05.026
|
31 |
SyrmosV L, Abdallah C T, DoratoP , GrigoriadisK. Static output feedback-a survey. Automatica, 1997, 33(2): 125–137
https://doi.org/10.1016/S0005-1098(96)00141-0
|
32 |
QiuJ, FengG, GaoH. Asynchronous output feedback control of networked nonlinear systems with multiple packet dropouts: T-S fuzzy affine model based approach. IEEE Transactions on Fuzzy Systems, 2011, 19(6): 1014–1030
https://doi.org/10.1109/TFUZZ.2011.2159011
|
33 |
WeiY, QiuJ, KarimiH R, Wang M. New results on ℋ∞ dynamic output feedback control for Markovian jump systems with time-varying delay and deficient mode information. Optimal Control Applications and Methods, 2014, 35(6): 656–675
https://doi.org/10.1002/oca.2093
|
34 |
ChenL, HuangX, FuS. Observer-based sensor fault-tolerant control for semi-Markovian jump systems. Nonlinear Analysis: Hybrid Systems, 2016, 22: 161–177
https://doi.org/10.1016/j.nahs.2016.04.003
|
35 |
XieL. Output feedback ℋ∞ control of systems with parameter uncertainty. International Journal of Control, 1996, 63(4): 741–750
https://doi.org/10.1080/00207179608921866
|
36 |
BoydS, El Ghaoui L, FeronE , BalakrishnanV. Linear Matrix Inequality in Systems and Control Theory. Philadelphia: Society for Industrial and Applied Mathematics, 1994
https://doi.org/10.1137/1.9781611970777
|
37 |
QiuJ, DingS X, GaoH, Yin S. Fuzzy-model-based reliable static output feedback ℋ∞ control of nonlinear hyperbolic PDE systems. IEEE Transaction on Fuzzy Systems, 2016, 24(2): 388–400
https://doi.org/10.1109/TFUZZ.2015.2457934
|
38 |
WeiY, QiuJ, LamH K, Wu L. Approaches to T-S fuzzy affine model based reliable output feedback control for nonlinear Itô stochastic systems. IEEE Transaction on Fuzzy Systems, doi: 10.1109/TFUZZ.2016.2566810
https://doi.org/10.1109/TFUZZ.2016.2566810
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|