PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2016 | 26 | 1 | 133-145
Tytuł artykułu

Stability analysis and $H_{∞}$ control of discrete T-S fuzzy hyperbolic systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T-S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and $H_{∞}$ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T-S fuzzy hyperbolic model with the discrete T-S fuzzy linear one are also given to illustrate the advantage of our approach.
Rocznik
Tom
26
Numer
1
Strony
133-145
Opis fizyczny
Daty
wydano
2016
otrzymano
2014-06-23
poprawiono
2014-12-17
poprawiono
2015-05-04
Twórcy
autor
  • School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
autor
  • School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
autor
  • School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
autor
  • Department of Mathematics, Huizhou University, Huizhou, Guangdong Province, 516007, China
autor
  • Department of Mathematics, Huizhou University, Huizhou, Guangdong Province, 516007, China
Bibliografia
  • Bemporad, A., Borrelli, F. and Morari, M. (2003). Min-max control of constrained uncertain discrete-time linear system, IEEE Transactions on Automatic Control 48(9): 1600-1606.
  • Cao, S.G., Rees, N.W., Feng, G. and Liu, W. (2000). $H_{∞}$ control of nonlinear discrete-time systems based on dynamical fuzzy models, International Journal of System Science 31(31): 229-241.
  • Cao, Y.Y. and Frank, P.M. (2000). Robust $H_{∞}$ disturbance attenuation for a class of uncertain discrete-time fuzzy systems, IEEE Transactions on Fuzzy Systems 8(4): 406-415.
  • Chen, B. and Liu, X.P. (2005). Delay-dependent robust $H_{∞}$ control for TCS fuzzy systems with time delay, IEEE Transactions on Fuzzy Systems 13(4): 544-556.
  • Chen, B.-S., Tseng, C.-S. and Uang, H.-J. (2000). Mixed $H₂/H_{∞}$ fuzzy output feedback control design for nonlinear dynamic systems: An LMI approach, IEEE Transactions on Fuzzy Systems 8(3): 249-265.
  • Chen, M.L. and Li, J.M. (2012). Modeling and control of T-S fuzzy hyperbolic model for a class of nonlinear systems, International Conference on Modelling, Identification and Control, Wuhan, China, pp. 57-62.
  • Chen, M.L. and Li, J.M. (2015). Non-fragile guaranteed cost control for Takagi-Sugeno fuzzy hyperbolic systems, International Journal of System Science 46(9): 1614-1627.
  • Datta, R., Bittermann, M.S., Deb, K. and Ciftcioglu, O. (2012). Probabilistic constraint handling in the framework of joint evolutionary-classical optimization with engineering application, IEEE Congress on Evolutionary Computation, Brisbane, Australia, pp. 1-8.
  • Du, D.S. (2012). Reliable $H_{∞}$ control for Takagi-Sugeno fuzzy systems with intermittent measurements, Nonlinear Analysis: Hybrid Systems 6(4): 930-941.
  • Elliott, D.L. (1999). Bilinear systems, Encyclopedia of Electrical Engineering, Wiley, New York, NY.
  • Feng, G. (2006). A survey on analysis and design of model-based fuzzy control systems, IEEE Transactions on Fuzzy Systems 14(5): 676-697.
  • Guan, X. and Chen, C. (2004). Delay-dependent guaranteed cost control for T-S fuzzy system with time delays, IEEE Transactions on Fuzzy Systems 12(2): 236-249.
  • Hsiao, M.Y., Liu, C.H., Tsai, S.H., Chen, P.S. and Chen, T.T. (2010). A Takagi-Sugeno fuzzy-model-based modeling method, IEEE International Conference on Fuzzy Systems, Barcelona, Spain, pp. 1-6.
  • Jadbabaie, A., Jamshidi, M. and Titli, A. (1998). Guaranteed-cost design of continuous-time Takagi-Sugeno fuzzy controllers via linear matrix inequalities, IEEE World Congress on Computational Intelligence, Anchorage, AK, USA, Vol. 1, pp. 268-273.
  • Kim, S.H., Lee, C.H. and Park, P.G. (2008). Relaxed delay-dependent stabilization conditions for discrete-time fuzzy systems with time delays, IEEE 10th International Conference on Control, Automation, Robotics and Vision, Hanoi, Vietnam, pp. 999-1004.
  • Li, J.M., Li, J., and Du, C.X. (2009). Linear Control System Theory and Methods, Xidian University Press, Xian, pp. 10-13.
  • Li, J.R., Li, J.M. and Xia, Z.L. (2011). Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays, International Journal of Applied Mathematics and Computer Science 21(4): 583-603, DOI: 10.2478/v10006-011-0046-6.
  • Li, J.R., Li, J.M. and Xia, Z.L. (2013a). Observer-based fuzzy control design for discrete-time T-S fuzzy bilinear systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 21(3): 435-454.
  • Li, J.R., Li, J.M. and Xia, Z.L. (2013b). Delay-dependent generalized H₂ fuzzy static-output-feedback control for discrete T-S fuzzy bilinear stochastic systems with mixed delays, Journal of Intelligent and Fuzzy Systems Applications in Engineering and Technology 25(4): 863-880.
  • Li, J.M. and Zhang, G. (2012). Non-fragile guaranteed cost control of T-S fuzzy time-varying state and control delays systems with local bilinear models, IEEE Transactions on Systems, Man and Cybernetics 9(2): 43-62.
  • Li, T.H.S. and Tsai, S.H. (2007). T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems, IEEE Transactions on Fuzzy Systems 15(3): 494-506.
  • Li, T.H.S. and Tsai, S.H. (2008). Robust $H_{∞}$ fuzzy control for a class of uncertain discrete fuzzy bilinear systems, IEEE Transactions on Systems, Man and Cybernetics B: Cybernetics 38(2): 510-527.
  • Li, T.H.S., Tsai, S.H., Lee, J.Z., Hsiao, M.Y. and Chao, C.H. (2008). Robust $H_{∞}$ fuzzy control for a class of uncertain discrete fuzzy bilinear systems, IEEE Transactions on Systems, Man and Cybernetics B: Cybernetics 38(2): 510-527.
  • Margaliot, M. and Langholz, G. (2003). A new approach to fuzzy modeling and control of discrete-time systems, IEEE Transactions on Fuzzy Systems 11(4): 486-494.
  • Mohler, R.R. (1973). Bilinear Control Processes, Academic Press, New York, NY.
  • Park, Y., Tahk, M.J. and Bang, H. (2004). Design and analysis of optimal controller for fuzzy systems with input constraint IEEE Transactions on Fuzzy System 12(6): 766-779.
  • Qi, R.Y., Tao, G., Jiang, B. and Tan, C. (2012). Adaptive control schemes for discrete-time T-S fuzzy systems with unknown parameters and actuator failures, IEEE Transactions on Fuzzy Systems 20(3): 471-486.
  • Qiu, J.B., Feng G. and Yang J. (2009). A new design of delay-dependent robust $H_{∞}$ filtering for discrete-time T-S fuzzy systems with time-varying delay, IEEE Transactions on Fuzzy Systems 17(5): 1044-1058.
  • Qiu, J.B., Feng G. and Gao H.J. (2010). Fuzzy-model-based piecewise $H_{∞}$ static-output-feedback controller design for networked nonlinear systems, IEEE Transactions on Fuzzy Systems 18(5): 919-934.
  • Siavash, F.D. and Alireza, F. (2014). Non-monotonic Lyapunov functions for stability analysis and stabilization of discrete time Takagi-Sugeno fuzzy systems, International Journal of Innovative Computing, Information and Control 10(4): 1567-1586.
  • Su, X.J., Shi P.G., Wu L.G. and Song Y.-D. (2013). A novel control design on discrete-time Takagi-Sugeno fuzzy systems with time-varying delays, IEEE Transactions on Fuzzy Systems 21(4): 655-671.
  • Su, X. J., Shi P., Wu L. and Basin M.V. (2014). Reliable filtering with strict dissipativity for T-S fuzzy time-delay systems, IEEE Transactions on Cybernetics 44(12): 2470-2483, DOI: 10.1109/TCYB.2014.2308983.
  • Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems, Man and Cybernetics 15(1): 116-132.
  • Tanaka, K. and Sugeno, M. (1992). Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems 45(2): 135-156.
  • Tanaka, K. and Wang, H.O. (2001). Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, Wiley, New York, NY.
  • Tong, S.C., He, X.L. and Zhang, H.C. (2009). A combined backstepping and small-gain approach to robust adaptive fuzzy output feedback control, IEEE Transactions on Fuzzy Systems 17(5): 1059-1069.
  • Tong, S.C., Huo, B.Y. and Li, Y.M. (2014). Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures, IEEE Transactions on Fuzzy Systems 22(1): 1-15.
  • Tong, S.C., Liu, C.L. and Li, Y.M. (2010). Fuzzy-adaptive decentralized output-feedback control for large-scale nonlinear systems with dynamical uncertainties, IEEE Transactions on Fuzzy Systems 18(5): 845-861.
  • Tong, S.C. and Li, Y.M. (2012). Adaptive fuzzy output feedback tracking backstepping control of strict-feedback nonlinear systems with unknown dead zones, IEEE Transactions on Fuzzy Systems 20(1): 168-180.
  • Tong, S., Yang, G. and Zhang, W. (2011). Observer-based fault-tolerant control against sensor failures for fuzzy systems with time delays, International Journal of Applied Mathematics and Computer Science 21(4): 617-627, DOI: 10.2478/v10006-011-0048-4.
  • Wang, J. (2014). Adaptive fuzzy control of direct-current motor dead-zone systems, International Journal of Innovative Computing, Information and Control 10(4): 1391-1399.
  • Yan, H.C., Zhang, H., Shi, H.B. and Meng, M.Q.-H. (2010). $H_{∞}$ fuzzy filtering for discrete-time fuzzy stochastic systems with time-varying delay, IEEE 29th Chinese Control Conference, Beijing, China, pp. 59993-59998.
  • Zhang, G. and Li, J.M. (2010). Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system, Journal of Systems Engineering and Electronics 21(4): 629-634.
  • Zhang, H.G. (2009). Fuzzy Hyperbolic Model: Modeling Control and Applications, Science Press, Beijing, pp. 121-131.
  • Zhang, H.G. and Quan, Y.B. (2001). Modeling, identification and control of a class of nonlinear system, IEEE Transactions on Fuzzy Systems 9(2): 349-354.
  • Zhang, H., Shi, Y., and Mehr, A.S. (2012). On filtering for discrete-time Takagi-Sugeno fuzzy systems, IEEE Transactions on Fuzzy Systems 20(2): 396-401.
  • Zhao, Y., and Gao, H.J. (2012). Fuzzy-model-based control of an overhead crane with input delay and actuator saturation Transactions on Fuzzy Systems 20(1): 181-186.
  • Zhao, T., Xiao, J., Li, Y. and Li, Y.X. (2013). A fuzzy Lyapunov function approach to stabilization of interval type-2 T-S fuzzy systems, IEEE 25th Chinese Control and Decision Conference, Xian, China, pp. 2234-2238.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv26i1p133bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.