In order to assure the stability of Takagi-Sugeno (T-S) fuzzy systems, the linear matrix inequality (LMI) should be applied. However, the LMI method cannot be applied online, because its computational complexity. In this paper, the T-S fuzzy control is transformed into a time-varying system. By using Riccati differential equation (RDE) and a special optimal-like controller, the T-S fuzzy control can be applied online. We prove that the T-S fuzzy control is stable and the trajectory tracking error converges to a bounded zone. Since RDE can be solved online, the novel T-S fuzzy control is adaptive and more simple and effective than LMI-based methods. We apply successfully this online fuzzy control to an autonomous underwater vehicle.
TakagiT. and SugenoM., Fuzzy identification of systems and its applications to modeling and control, IEEE Trans Syst, Man, Cybern15(1) (1985), 116–132.
2.
DasP.C., Statistically convergent fuzzy sequence spaces by fuzzy metric, Kyungpook Math Journal54(3) (2014), 413–423.
3.
TripathyB.C. and RayG.C., Weakly continuous functions on mixed fuzzy topological spaces, Acta Scientiarum Technology36(2) (2014), 331–335.
4.
FengG., A survey on analysis and design of model-based fuzzy control systems, IEEE Trans Fuzzy Syst14(5) (2006), 676–697.
5.
TanakaK., HoriT. and WangH.O., A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Trans Fuzzy Syst11(4) (2003), 582–589.
6.
TanakaK. and WangH.O., Fuzzy control systems design and analysis: A linear matrix inequality approach, John Wiley & Sons Inc., New York, USA, 2004.
7.
TuanH.D., ApkarianP., NarikiyoT. and YamamotoY., Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Trans, Fuzzy Syst9 (2001), 324–332.
8.
TsengC.-S., ChenB.-S. and UangH.-J., Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model, IEEE Trans Fuzzy Syst9(3) (2001), 381–392.
9.
LiuX. and ZhangQ., Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems, IEEE Trans Fuzzy Syst11(6) (2003), 830–839.
10.
LeeH.-J., KimH., JooY.-H., ChangW. and ParkJ.-B., A new intelligent digital redesign for T-S fuzzy systems: Global approach, IEEE Trans Fuzzy Syst12(2) (2004), 274–284.
11.
WangW.-J. and LinW.-W., Decentralized PDC for large-scale T-S fuzzy systems, IEEE Trans Fuzzy Syst13(6) (2005), 381–392.
12.
DongJ. and YangG.-H., H∞ controller synthesis via switched PDC scheme for discrete-time T-S fuzzy systems, IEEE Trans Fuzzy Syst17(3) (2009), 544–555.
13.
ZhaoY., ZhangC. and GaoH., New approach to guaranteed cost control of T-S fuzzy dynamic systemsWith interval parameter uncertainties, IEEE Trans Syst, Man, Cybern, B, Cybern39(6) (2009), 1516–1527.
14.
XieX., YueD., MaT. and ZhuX., Further studies on control synthesis of discrete-time T-S fuzzy systems via augmented multi-indexed matrix approach, IEEE Trans Cybern44(12) (2014), 2784–2791.
15.
WuL., SuX., ShiP. and QiuJ., A new approach to stability analysis and stabilization of discrete-time T-S fuzzy time varying delay systems, IEEE Trans Syst, Man, Cybern, B, Cybern41(1) (2011), 273–286.
16.
SuX., ShiP., WuL. and SongY.-D., A novel control design on discrete-time takagi–sugeno fuzzy systems with time-varying delays, IEEE Transactions on Fuzzy Systems21(4) (2013), 655–671.
17.
SuX., WuL., ShiP. and SongY.-D., A novel approach to output feedback control of fuzzy stochastic systems, Automatica50(12) (2014), 3268–3275.
18.
LinC., WangQ.-G. and LeeT.-H., Output tracking control for nonlinear systems via T-S fuzzy model approach, IEEE Trans Syst, Man, Cybern, B, Cybern36(2) (2004), 450–457.
19.
ChiuC.-S., T-S fuzzy maximum power point tracking control of solar power generation systems,–, IEEE Trans Energy Convers25(4) (2010), 1123–1132. 7.
20.
LiN. and LiS.-Y., Stability analysis and design of T-S fuzzy control system with simplified linear rule consequent, IEEE Trans Syst, Man, Cybern, B, Cybern34(1) (2004), 799–795.
21.
NarendraK.S. and BalakrishnanJ., The changing face of adaptive control: The use of multiple models, Annual Reviews in Control35(1) (2011), 1–12.
22.
JohJ., ChenY.-H. and LangariR., On the stability issues of linear Takagi-Sugeno fuzzy models, IEEE Trans Fuzzy Syst6 (1998), 402–410.
23.
JohanssonM., RantzerA. and ArzenK.E., Piecewise quadratic stability of fuzzy systems, IEEE Trans Fuzzy Syst7 (1999), 713–722.
24.
ZhaoX., ZhangL., ShiP. and KarimiH.R., Novel stability criteria for T–S fuzzy systems, IEEE Trans Fuzzy Syst22(2) (2014), 313–323.
25.
QiuJ., FengG. and GaoH., Static-output-feedback H∞ control of continuous-time T-S fuzzy affine systems via piecewise lyapunov functions, IEEE Trans Fuzzy Syst21(2) (2013), 245–3261.
26.
WangW.-J. and SunC.-H., A relaxed stability criterion for T-S fuzzy discrete systems, IEEE Trans Syst, Man, Cybern, B, Cybern34(5) (2004), 2155–2158.
27.
LinP.-T., WangC.-H. and LeeT.-T., Time-optimal control of TS fuzzy models via lie algebra, IEEE Trans Fuzzy Syst17(4) (2009), 737–749.
28.
ChangY.-H., ChanW.-S. and ChangC.-W., T-S fuzzy model-based adaptive dynamic surface control for ball and beam system, IEEE Trans Ind Electron60(6) (2013), 2251–2263.
29.
GaoQ., FengG. and XiZ., A new design of robust H∞ sliding mode control for uncertain stochastic T-S fuzzy time-delay systems, IEEE Trans Cybern44(9) (2014), 1556–1566.
30.
FengG., Analysis and Synthesis of Fuzzy Control Systems: A Model-Based Approach, CRC Press, Boca Roton, USA, 2010.
31.
WuS.-J. and LinC.-T., Optimal fuzzy controller design in continuous fuzzy system: Global concept approach, IEEE Transactions on Fuzzy Systems8(6) (2000), 713–729.
32.
PoznyakA.S., SanchezE.N. and YuW., Differential Neural Networks for Robust Nonlinear Control, World Scientific Publishing Co., Singapore, 2001.
33.
WillemsJ.C., Least squares optimal control and algebraic riccati equations, IEEE Transactions on Automatic Control16(2) (1971), 621–634.
34.
YuW. and LiX., Fuzzy identification using fuzzy neural networks with stable learning algorithms, IEEE Transactions on Fuzzy Systems12(3) (2004), 411–420.
35.
ChangW.-J., ChangW. and LiuH.-H., Model-based fuzzy modeling and control for autonomous underwater vechicles in the horizonal plane, Journal of Marine Science and Technology11(3) (2003), 155–163.
36.
LefeberE., PettersenK.Y. and NijmeijerH., Tracking control of an underactuated ship, IEEE Transactions on Control Systems Technology11(1) (2003), 52–61.
37.
WimmerH.K., Monotonicity of maximal solutions of algebraic riccati equations, System and Control Letters5(4) (1985), 317–319.
