Stability analysis and constrained fuzzy tracking control of positive nonlinear systems

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• 作者：Xiaolong Zheng ; Xinyong Wang ; Yunfei Yin ; Lili Hu
• 关键词：Positive nonlinear systems ; T–S fuzzy system ; Quadratic copositive Lyapunov function ; Constrained tracking control
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：83
• 期：4
• 页码：2509-2522
• 全文大小：845 KB
• 参考文献：1.Farina, L., Rinaldi, S.: Positive Linear Systems. Wiley Interscience Series, New York (2000)CrossRef
  2.Zhao, X., Liu, X., Yin, S., Li, H.: Improved results on stability of continuous-time switched positive linear systems. Automatica 50(2), 614–621 (2014)CrossRef
  3.Shen, J., Lam, J.: \({L}_{\infty }\) -gain analysis for positive systems with distributed delays. Automatica 50(1), 175–179 (2014)CrossRef
  4.Liu, X., Dang, C.: Stability analysis of positive switched linear systems with delays. IEEE Trans. Automat. Control. 56(7), 1684–1690 (2011)CrossRef
  5.Rami, M. A.: Stability analysis and synthesis for linear positive systems with time-varying delays. In: Proceedings of the 3rd Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2009), pp 205–215 (2009)
  6.Kaczorek, T.: Realization problem for positive linear systems with time delay. Math. Probl. Eng. 2005(5), 455–463 (2005)CrossRef
  7.Commault, C.: A simple graph theoretic characterization of reachability for positive linear systems. Syst. Control Lett. 52(3), 275–282 (2013)
  8.Mason, O., Shorten, R.: On linear copositive Lyapunov functions and the stability of switched positive linear systems. IEEE Trans. Automat. Control. 52(7), 1346–1349 (2007)CrossRef
  9.Zhao, X., Zhang, L., Shi, P., Liu, M.: Stability of switched positive linear systems with average dwell time switching, and design. Automatica 48(6), 1132–1137 (2012)CrossRef
  10.Zhao, X., Yin, S., Li, H., Niu, B.: Switching stabilization for a class of slowly switched systems. IEEE Trans. Automat. Control. 60(1), 221–226 (2015)CrossRef
  11.Zhao, X., Zhang, L., Shi, P., Liu, M.: Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Automat. Control. 57(7), 1809–1815 (2012)CrossRef
  12.Liu, H., Zhao, X.: Finite-time \(H_{\infty }\) control of switched systems with mode-dependent average dwell time. J. Franklin Inst. 351(3), 1301–1315 (2014)CrossRef
  13.Liu, H., Shen, Y., Zhao, X.: Asynchronous finite-time \(H_{\infty }\) control for switched linear systems via mode-dependent dynamic state-feedback. Nonlinear Anal. Hybrid Syst. 8, 109–120 (2013)CrossRef
  14.Zhao, X., Liu, H., Zhang, J.: Multiple-mode observer design for a class of switched linear systems linear systems. IEEE Trans. Automat. Sci. Eng. 12(1), 272–280 (2015)CrossRef
  15.Feng, J., Lam, J., Li, P., Shu, Z.: Decay rate constrained stabilization of positive systems using static output feedback. Int. J. Robust Nonlinear Control. 21, 44–54 (2011)CrossRef
  16.Shu, Z., Lam, J., Gao, H., Du, B., Wu, L.: Positive observers and dynamic output-feedback controllers for interval positive linear systems. IEEE Trans. Circuits Syst. I Regul. Pap. 55(10), 3209–3222 (2008)CrossRef
  17.Li, P., Lam, J., Wang, Z., Date, P.: Positivity-preserving \({H}_{\infty }\) model reduction for positive systems. Automatica 47(7), 1504–1511 (2011)CrossRef
  18.Imsland, L., Eikrem, G.O., Foss, B.A.: A state feedback controller for a class of nonlinear positive systems applied to stabilization of gas-lifted oil wells. N Control Eng. Pract. 3, 7–15 (2006)
  19.Fadali, M.S., Jafarzadeh, S.: Stability analysis of positive interval type-2 TSK systems with applications to energy markets. IEEE Trans. Fuzzy Syst. 22(4), 1031–1038 (2014)CrossRef
  20.Tong, S., Li, H.: Fuzzy adaptive sliding-mode control for MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 11(3), 354–360 (2003)CrossRef
  21.Tong, S., Chen, B., Wang, Y.: Fuzzy adaptive output feedback control for MIMO nonlinear systems. Fuzzy Sets Syst. 156(2), 285–299 (2005)CrossRef
  22.Liu, Y., Tong, S., Chen, C.L.P.: Adaptive fuzzy control via observer design for uncertain nonlinear systems with unmodeled dynamics. IEEE Trans. Fuzzy Syst. 21(2), 275–288 (2013)CrossRef
  23.Niknam, T., Khooban, M., Kavousifard, A., Soltanpour, M.: An optimal type II fuzzy sliding mode control design for a class of nonlinear systems. Nonlinear Dyn. 75(1–2), 73–83 (2014)CrossRef
  24.Vembarasan, V., Balasubramaniam, P.: Chaotic synchronization of Rikitake system based on TS fuzzy control techniques. Nonlinear Dyn. 74(1–2), 31–44 (2013)CrossRef
  25.Taieb, N., Hammami, M., Delmotte, F., Ksontini, M.: On the global stabilization of Takagi–Sugeno fuzzy cascaded systems. Nonlinear Dyn. 67(4), 2847–2856 (2012)CrossRef
  26.Lam, H.K., Sorimachi, K.: Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach. IEEE Trans. Syst. Man Cybern. Part B 42(1), 258–267 (2012)CrossRef
  27.Zhao, X., Zhang, L., Shi, P., Karimi, H.R.: Novel stability criteria for T–S fuzzy systems. IEEE Trans. Fuzzy Syst. 22(2), 313–323 (2014)CrossRef
  28.Shi, P., Luan, X., Liu, F.: \({H}_{\infty }\) filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Trans. Ind. Electron. 59(6), 2732–2739 (2012)CrossRef
  29.Chen, B., Liu, X., Liu, K., Shi, P.: Direct adaptive fuzzy control for nonlinear systems with time-varying delays. Info. Sci. 180(5), 776–792 (2010)CrossRef
  30.Pan, Y., Furuta, K.: Control synthesis of continuous-time TS fuzzy systems with local nonlinear models. IEEE Trans. Syst. Man Cybern. Part B 39(5), 1245–1258 (2006)
  31.Assawinchaichote, W., Shi, P., Nguang, S.K.: Fuzzy \({H}_{\infty }\) output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach. IEEE Trans. Fuzzy Syst. 14(3), 361–371 (2006)CrossRef
  32.Jiang, B., Mao, Z., Shi, P.: \({H}_{\infty }\) -filter design for a class of networked control systems via T-S fuzzy-model approach. IEEE Trans. Fuzzy Syst. 18(1), 201–208 (2010)CrossRef
  33.Assawinchaichote, W., Nguang, S.K., Shi, P.: \({H}_{\infty }\) output feedback control design for uncertain fuzzy singularly perturbed systems: an LMI approach. Automatica 40(12), 2147–2152 (2004)
  34.Liu, M., Cao, X., Shi, P.: Fault estimation and tolerant control for fuzzy stochastic systems. IEEE Trans. Fuzzy Syst. 21(2), 221–229 (2013)CrossRef
  35.Zhang, J., Shi, P., Xia, Y.: Robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties. IEEE Trans. Fuzzy Syst. 18(4), 700–711 (2010)CrossRef
  36.Zhang, J., Shi, P., Xia, Y.: Fuzzy delay compensation control for TS fuzzy systems over network. IEEE Trans. Syst. Man Cybern. Part B 41(3), 259–268 (2012)
  37.Liu, Y., Tong, S., Li, T.: Observer-based adaptive fuzzy tracking control for a class of uncertain nonlinear MIMO systems. Fuzzy Sets Syst. 161(1), 25–44 (2011)CrossRef
  38.El Hajjaji, A., Chadli, M.: Commande basée sur la mod élisation floue de type Takagi-Sugeno d’un procédé expé rimental à quatre cuves. Rev. Sci. Technol. Automat. e-STA. 6(3), 46–51 (2009)
  39.Benzaouia, A., El Hajjaji, A.: Delay-dependent stabilization conditions of controlled positive T–S fuzzy systems with time varying delay. Int. J. Innov. Comput. Info. Control 7(4), 1533–1547 (2011)
  40.Benzaouia, A., Hmamed, A., EL Hajjaji, A.: Stabilization of controlled positive discrete-time T–S fuzzy systems by state feedback control. Int. J. Adapt. Control Signal Process. 48(6), 1132–1137 (2012)
  41.Benzaouia, A., Oubah, R., El Hajjaji, A., Tadeo, F.: Stability and stabilization of positive Takagi-Sugeno fuzzy continuous systems with delay. In: 50th IEEE Conference on Decision and Control, Orlando, FL, pp 8279–8284 (2011)
  42.Mao, Y., Zhang, H., Dang, C.: Stability analysis and constrained control of a class of fuzzy positive systems with delays using linear copositive lyapunov functional. Circuits Syst. Signal Process. 31(5), 1863–1875 (2012)CrossRef
  43.Johansson, M., Rantzer, A., Arzen, K.: Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst. 7, 713–722 (1999)CrossRef
  44.Zhao, X., Zhang, L., Shi, P., Karimi, H.: Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits. IEEE Trans. Ind. Electron. 61(8), 4161–4170 (2014)CrossRef
  45.Zhao, X., Zhang, L., Shi, P.: Stability of a class of switched positive linear time-delay systems. Int. J. Robust. Nonlin. 23(5), 578–589 (2013)CrossRef
  
• 作者单位：Xiaolong Zheng (1) (2)
  Xinyong Wang (1) (2)
  Yunfei Yin (1) (2)
  Lili Hu (1) (2)
  
  1. College of Engineering, Bohai University, Jinzhou, 121013, China
  2. Chongqing SANY High-Intelligent Robots Co. Ltd., Chongqing, China
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

This paper is concerned with stability and tracking control of positive nonlinear systems via Takagi–Sugeno (T–S) fuzzy modeling. Firstly, some less conservative stability conditions for positive nonlinear systems that can be represented by a class of positive T–S fuzzy model with only nonnegative state variables are derived by proposing the so-called quadratic copositive Lyapunov functions. Secondly, a constrained control via the parallel distributed compensation scheme is designed to stabilize a positive nonlinear system, while imposing positivity in closed loop, upon which a constrained fuzzy tracking controller is also given to guarantee the tracking performance and positivity in closed loop. Finally, a numerical example is provided to show the advantages of the proposed methods, and an example of a real plant is presented to demonstrate the controller design scheme. Keywords Positive nonlinear systems T–S fuzzy system Quadratic copositive Lyapunov function Constrained tracking control