ROBUST CONTROLLER DESIGN OF SINGULARLY PERTURBATION SYSTEMS WITH ACTUATOR SATURATION VIA DELTA OPERATOR APPROACH

Yang Wang, Yiyong Yang, and Fuchun Sun

References

  1. [1] Y. Yuan, F. Sun, H. Liu, and Q. Wang, Multi-objective robustcontrol of flexible-link manipulators based on fuzzy singularlyperturbed model with multiple perturbation parameters, IEEE2012 31st Chinese Control Conf. (CCC), Hefei, China, 2012,2613–2617.
  2. [2] L. Li and F. Sun, The direct adaptive control based on thesingularly perturbed model with the unknown consequenceparameters, International Journal of Control, Automation,and Systems, 8(2), 2010, 238–243.
  3. [3] H. Bolandi, S.M. Esmaeilzadeh, Exact tip trajectory trackingcontrol of a flexible robot arm, International Journal of ControlAutomation & Systems, 26(1), 2011, 100–109.
  4. [4] I. Motte and G. Campion, A slow manifold approach forthe control of mobile robots not satisfying the kinematicconstraints, IEEE Transactions on Robotics and Automation,16(6), 2000, 875–880.
  5. [5] J.W. Kimball and P.K. Krein, Singular perturbation theory forDC-DC converters and application to PFC converters, IEEETransactions on Power Electronics, 23(6), 2008, 2970–2981.
  6. [6] H. Jia, X.D. Zhang, H.X. Sun et al., Active control of spaceflexible-joint/flexible-link manipulator, Proc. 1st IEEE Conf.Robotics Automation and Mechatronics, Chengdu, China, 2008,812–818.
  7. [7] Z. Gajic and M.T. Lim, Optimal control of singularly perturbedlinear systems and applications high accuracy techniques, (NewYork: Marcel Dekker, Inc., 2001).
  8. [8] J.H. Chow and P.V. Kokotovic, A decomposition of near-optimum regulators for systems with slow and fast modes, IEEETransactions on Automatic Control, 21(5), 1976, 701–705.
  9. [9] X.Y. Zhang, H.Z. Jin, H.P. Zhang, G.B. Li and M. Ji, Robustsliding mode control for a class of uncertain nonlinear singularlyperturbed systems, Proc. 41st SICE Annual Conf. IEEE,Osaka, Japan, 2002, 2616–2621.
  10. [10] H.P. Liu, F.C. Sun and K.Z. He, Survey of singularly perturbedcontrol systems: Theory and application, Control Theory andApplications, 20(1), 2003, 1–7.
  11. [11] P.V. Kokotovic and R.A. Yackel, Singular perturbation of linearregulators: Basic theorems, IEEE Transactions on AutomaticControl, 17(1), 1972, 29–37.
  12. [12] Y.Y. Wang, S.J. Shi and Z.J. Zhang, A descriptor-systemapproach to singular perturbation of linear regulators, IEEETransactions on Automatic Control, 33(4), 1988, 370–373.
  13. [13] H. Xu, H. Mukaidani and K. Mizukami, New method forcomposite optimal control of singularly perturbed systems,International Journal of Systems Science, 28(2), 1997,161–172.
  14. [14] Z. Gajic, M.T. Lim and J. Bentsman, Optimal controlof singularly perturbed linear systems and applications:High-accuracy techniques, Applied Mechanics, 55(3), 2002,1339–1343.
  15. [15] J.H. Chow and P.V. Kokotovic, A decomposition of near-optimum regulators for systems with slow and fast modes, IEEETransactions on Automatic Control, 21(5), 1976, 701–705.
  16. [16] J.-J.E. Slotine and J.A. Coetsee, Adaptive sliding controllersynthesis for non-linear systems, International Journal ofControl, 43(6), 1986, 1631–1651.
  17. [17] G. Xia, A. Zhao, H. Wu, et al., Adaptive robust output feedbacktrajectory tracking control for ships with input nonlinearities,International Journal of Control Automation & Systems, 31(4),2016, 341–353.
  18. [18] T. Huang, P. Yang, K. Yang, et al., Navigation of mobile robotin unknown environment based on TS neuro-fuzzy system,International Journal of Control Automation & Systems, 30(4),2015, 384–396.
  19. [19] Y.N. Hu, Y. Yuan, H.B. Min et al., Multi-objective robustcontrol based on fuzzy singularly perturbed models for hypersonic vehicles, Science China Information Sciences, 54(3),2011, 563–576.
  20. [20] L. Li and F. Sun, An adaptive tracking controller design fornon-linear singularly perturbed systems using fuzzy singularlyperturbed model, IMA Journal of Mathematical Control andInformation, 26(4), 2009, 395–415.
  21. [21] T.M. Guerra, M. Bernal, K. Guelton, et al., Non-quadraticlocal stabilization for continuous-time Takagi-Sugeno models,Fuzzy Sets & Systems, 201(12), 2012, 40–54.
  22. [22] N. Vafamand and M.S. Sadeghi, More relaxed non-quadraticstabilization conditions for TS fuzzy control systems using LMIand GEVP, International Journal of Control, Automation andSystems, 13(4), 2015, 995–1002.
  23. [23] N. Vafamand and M. Shasadeghi, More relaxed non-quadraticstabilization conditions using TS open loop system and controllaw properties, Asian Journal of Control, 19, 2017, 1–15.
  24. [24] H. Yenan, S. Fuchun, L. Huaping et al., ε-Dependent controllability for two time-scale systems, Tsinghua Science &Technology, 14(2), 2009, 271–280.
  25. [25] H. Liu, F. Sun, and Z. Sun, Stability analysis and synthesisof fuzzy singularly perturbed systems, IEEE Transactions onFuzzy Systems, 13(2), 2005, 273–284.
  26. [26] T. Hu and Z. Lin, Control system with actuator saturation:Analysis and design, (Boston: Birkhu¨aser, 2001).
  27. [27] H. Long and J. Zhao, Anti-disturbance inverse optimal attitudecontrol design for flexible spacecraft with input saturation, 201411th World Congress on Intelligent Control and Automation(WCICA), Shenyang, China, 2014, 2961–2966.
  28. [28] M. Jiang, H. He, and P. Xiong, Anti-windup for time varyingdelayed cellular neural networks subject to input saturation,2014 Fifth International Conf. Intelligent Control and Processing (ICICIP), Dalian, China, 18–20 Aug. 2014, 485–491.
  29. [29] Z. Zhao, Y. Hong, and Z. Lin, Simi-global output consensusof linear agents with external disturbances and actuator saturation: An output regulation approach, 2014 33rd ChineseControl Conference (CCC), Nanjing, China, 28–30 July 2014,5727–5732.
  30. [30] C. Yang, L. Ma, X. Ma, and L. Zhou, Control of singularly perturbed system subject to actuator saturation, 2014 11th WorldCongress on Intelligent Control and Automation (WCICA),Shenyang, China, June 29 2014–July 4 2014, 1711–1716.
  31. [31] P. Shi, Y. Yin, and F. Liu, Gain-scheduled worst case controlon nonlinear stochastic system subject to actuator saturationand unknown information, Journal of Optimization Theoryand Applications, 156(3), 2013, 844–858.
  32. [32] T. Shi and H. Su, Sampled-data MPC for LPV systems withstate saturation, IET Control Theory and Applications, 8(17),2014, 1781–1788.
  33. [33] X. Wang, A. Saberi, and A. A. Stoorvogel, Stabilization ofdiscrete-time linear systems subject to input saturation andmultiple unknown constant delays, IEEE Transactions onAutomatic Control, 59(6), 2014, 1667–1672.
  34. [34] H. Su and M.Z.Q. Chen, Multi-agent containment control withinput saturation on switching topologies, IET Control Theoryand Applications, 9(3), 2015, 399–409.
  35. [35] F. Wu, Q. Zheng, and Z. Lin, Disturbance attenuation by output feedback for linear systems subject to actuator saturation,International Journal of Robust and Nonlinear Control, 19(2),2009, 168–184.
  36. [36] R. Middleton and G. Goodwin, Improved finite word lengthcharacteristics in digital control using delta operators, IEEETransactions on Automatic Control, 31(11), 1986, 1015–1021.
  37. [37] H. Yang, Y. Xia, P. Shi et al., Analysis and synthesis of deltaoperator systems, (Berlin Heidelberg: Springer, 2012).
  38. [38] H. Yang, P. Shi, Z. Li et al., Analysis and design for delta operator systems with actuator saturation, International Journalof Control, 87(5), 2014, 987–999.
  39. [39] H. Yang, Y. Xia and P. Shi, Observer-based sliding mode controlfor a class of discrete systems via delta operator approach,Journal of the Franklin Institute, 347(7), 2010, 1199–1213.
  40. [40] H. Yang, Y. Xia, P. Shi, and M. Fu, Stability of Markovian jumpsystems over networks via delta operator approach, Circuits,Systems and Signal Processing, 31(1), 2012, 107–125.
  41. [41] H. Yang, Y. Xia, and P. Shi, Observer-based sliding modecontrol for a class of discrete systems via delta operatorapproach, Journal of the Franklin Institute, 347(7), 2010,1199–1213.
  42. [42] H. Yang, X. Li, Z. Liu et al., Robust fuzzy-scheduling control for nonlinear systems subject to actuator saturation viadelta operator approach, Information Sciences, 272(3), 2014,158–172.
  43. [43] H. Yang, Y. Xia, P. Shi, and M. Fu, Stability analysis for highfrequency networked control systems, IEEE Transactions onAutomatic Control, 57(10), 2012, 2694–2700.
  44. [44] T. Takagi and M. Sugeno, Fuzzy identification of systems andits applications to modeling and control, IEEE Transactionson Fuzzy System, 15, 1985, 116–132.
  45. [45] L. Zhou, Q. Zhang, Y. Hu et al., Stability analysis and synthesisof TS fuzzy systems, Control Theory & Applications, 24(6),2007, 886–890.
  46. [46] K. Tanaka, T. Hori, and H.O. Wang, A multiple Lyapunovfunction approach to stabilization of fuzzy control systems,IEEE Transactions on Fuzzy Systems, 11(4) 2003, 582–589.

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