Forwarding-based immersion and invariance control for \(\varvec{n}\) -dimensional strict-feedback nonlinear systems

详细信息    查看全文

• 作者：Xu Zhang ; Xianlin Huang ; Hongqian Lu ; Hongyang Zhang
• 关键词：n ; Dimensional nonlinear systems ; Feedback form ; Immersion and invariance (I&I ) ; Forwarding design ; Mappings ; Virtual controls
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：83
• 期：1-2
• 页码：483-496
• 全文大小：878 KB
• 参考文献：1.Astolfi, A., Ortega, R.: Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Trans. Autom. Control 48(4), 590鈥?06 (2003)CrossRef MathSciNet
  2.Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, New York (1995)CrossRef
  3.Olfati-Saber, R.: Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles. Ph.D. thesis, Massachusetts Institute of Technology, pp. 152鈥?53 (2001)
  4.Liu, X., Ortega, R., Su, H., Chu, J.: Immersion and invariance adaptive control of nonlinear parameterized nonlinear systems. IEEE Trans. Autom. Control 55(9), 2209鈥?214 (2010)CrossRef MathSciNet
  5.Sonneveldt, L.,van Oort, E.R., Chu, Q.P., Mulder, J.A.: Immersion and invariance based nonlinear adaptive flight control. In: AIAA Guidance, Navigation, and Control Conference, Toronto, Ontario Canada (2010)
  6.Tagne, G., Taji, R., Charara. A.: Immersion and invariance control for reference trajectory tracking of autonomous vehicles. In: Proceedings of 16th IEEE Annual Conference on Intelligent Transportation Systems, Hague, Netherlands, pp. 2322鈥?328 (2013)
  7.Xie, Q., Han, Z., Wang, H., Zhang, W.: Stabilization of center systems via immersion and invariance. Nonlinear Dyn. 57(3), 313鈥?19 (2009)CrossRef MathSciNet
  8.Kemmetm眉ller, W., Kugi, A.: Immersion and invariance-based impedance control for electrohydraulic systems. Int. J. Robust Nonlinear Control 20(7), 725鈥?44 (2010)CrossRef
  9.Lee, K., Singh, S.: Immersion and invariance-based adaptive control of a nonlinear aeroelastic system. J. Guid Control Dyn. 32(4), 1100鈥?110 (2009)CrossRef
  10.Hu, J., Zhang, H.: Immersion and invariance based command-filtered adaptive backstepping control of VTOL vehicles. Automatica 49, 2160鈥?167 (2013)CrossRef
  11.Astolfi, A., Karagiannis, D., Ortega, R.: Towards applied nonlinear adaptive control. Annu. Rev. Control 32(2), 136鈥?48 (2008)CrossRef
  12.Rapp, P., Kl眉nder, M., Sawodny, O., Tar铆n, C.: Nonlinear adaptive and tracking control of a pneumatic actuator via immersion and invariance. In: Proceedings of 51st IEEE Conference on Decision and Control, Maui, Hawaii, USA, pp. 4145鈥?151 (2012)
  13.Manjarekar, N.S., Banavar, R.N., Ortega, R.: Stabilization of a synchronous generator with a controllable series capacitor via immersion and invariance. Int. J. Robust Nonlinear Control 22(8), 858鈥?74 (2012)CrossRef MathSciNet
  14.Thomas, W., Christian, O., Gerd, H.: Immersion and invariance control for an antagonistic joint with nonlinear mechanical stiffness. In: Proceedings of 49th IEEE Conference on Decision and Control, Atlanta, GA, USA, pp. 1128鈥?135 (2010)
  15.Acosta, J.脕., Ortega, R., Astolfi, A.: A constructive solution for stabilization via immersion and invariance: the cart and pendulum system. Automatica 44(9), 2352鈥?357 (2008)CrossRef MathSciNet
  16.Sarras, I., Siguerdidjane, H.B., Ortega, R.: Stabilization of the experimental Cart鈥揚endulum system with proven domain of attraction. Eur. J. Control 16(4), 329鈥?40 (2010)CrossRef MathSciNet
  17.Monfared, O., Khayatian, A., Mahzoon, M., Karimaghaee, P.: Immersion and invariance adaptive control of a class of nonlinear systems with unknown control direction. Int. J. Syst. Sci. 44(12), 2287鈥?294 (2013)CrossRef MathSciNet
  18.Sarras, I., Acosta, J.脕., Ortega, R.: Constructive immersion and invariance stabilization for a class of underactuated mechanical systems. Automatica 49(5), 1442鈥?448 (2013)CrossRef MathSciNet
  19.Karagiannis, D., Astolfi, A.: Nonlinear adaptive control of systems in feedback form: an alternative to adaptive backstepping. Syst. Control Lett. 57(9), 733鈥?39 (2008)CrossRef MathSciNet
  20.Yal莽in, Y., Astolfi, A.: Immersion and invariance adaptive control for discrete time systems in strict feedback form. Syst. Control Lett. 61(12), 1132鈥?137 (2012)CrossRef
  21.Liu, H.T., Wang, X.Z., Zhang, T.: Robust finite-time control of a class of high-order uncertain nonlinear systems. Asian J. Control 17(3), 1081鈥?087 (2015)CrossRef MathSciNet
  22.Wang, H., Zhu, Q.X.: Finite-time stabilization of high-order stochastic nonlinear systems in strict-feedback form. Automatica 54, 284鈥?91 (2015)CrossRef
  23.Zhang, X.H., Xie, X.J., Huang, Y.X.: Global state feedback stabilization of high-order nonlinear systems with multiple time-varying delays. J. Frankl. Inst. 352(1), 271鈥?90 (2015)CrossRef MathSciNet
  24.Zhang, H.W., Lewis, F.L.: Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics. Automatica 48(7), 1432鈥?439 (2012)CrossRef MathSciNet
  25.Sun, Z.Y., Liu, Y.G.: Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems. Automatica 43(10), 1772鈥?783 (2007)CrossRef MathSciNet
  26.Sepulchre, R., Jankovic, M., Kokotovic, P.V.: Integrator forwarding: a new recursive nonlinear robust design. Automatica 33(5), 979鈥?84 (1997)CrossRef MathSciNet
  27.She, J.H., Zhang, A.C., Lai, X.Z.: Global stabilization of 2-DOF underactuated mechanical systemsan equivalent-input-disturbance approach. Nonlinear Dyn. 69(1鈥?), 495鈥?09 (2012)CrossRef MathSciNet
  28.Astolfi, A., Karagiannis, D., Ortega, R.: Nonlinear and Adaptive Control with Applications. Springer, New York (2008)CrossRef
  
• 作者单位：Xu Zhang (1)
  Xianlin Huang (1)
  Hongqian Lu (1)
  Hongyang Zhang (1)
  
  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, Hei Longjiang, 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

Implementation of immersion and invariance (I&I) theorem becomes increasingly difficult as the degree of freedom increases. This inherent difficulty is mainly driven by the need to solve the partial differential equations in the immersion conditions. For a class of n-dimensional nonlinear systems in strict-feedback form, a novel method for designing asymptotically stabilizing control laws is developed in this work. At each step of the design, by defining a lower-order target system, the required mappings can be transformed into the virtual control inputs and the controlled system is able to exhibit the same responses as the target system. The order of nonlinear systems is reduced step by step by implementing I&I theorem repetitively. Unlike other control methodologies, the proposed algorithm does not require knowledge of Lyapunov functions in principle. In this paper, the design procedure and proof of closed-loop stability are described in detail. The TORA and magnetic levitation system are used to demonstrate the design procedures and controller performance via various simulations. Keywords n-Dimensional nonlinear systems Feedback form Immersion and invariance (I&I ) Forwarding design Mappings Virtual controls