Kybernetika 50 no. 3, 450-469, 2014

Constraint robust adaptive stabilization for a class of lower triangular systems with unknown control direction

Jianglin Lan, Weijie Sun and Yunjian PengDOI: 10.14736/kyb-2014-3-0450

Abstract:

This paper studies the constrained robust adaptive stabilization problem for a class of lower triangular systems with unknown control direction. A robust adaptive feedback control law for the systems is proposed by incorporating the technique of Barrier Lyapunov Function with Nussbaum gain. Such a controlled system arises from the study of the constrained robust output regulation problem for a class of output feedback systems with the unknown control direction and a nonlinear exosystem. An application of the constrained robust adaptive stabilization design leads to the solution of the constrained robust output regulation problem in the sense that the output tracking error is constrained within the prescribed barrier limit while asymptotically approaching to zero and the closed loop signals are all bounded for all the time. A numerical example is provided to illustrate the performance of the proposed control.

Keywords:

output regulation, nonlinear exosystem, Nussbaum gain, Barrier Lyapunov Function

Classification:

93E12, 62A10

paper.pdf

References:

  1. S. Čelikovský and J. Huang: Continuous feedback practical output regulation for a class of nonlinear systems having nonstabilizable linearization. In: Proc. IEEE Conference on Decision and Control 1999, Phoenix 1999.   CrossRef
  2. B. Castillo-Toledo, S. Čelikovský and S. Digennaro: Generalized immersion and nonlinear robust output regulation problem. Kybernetika 40 (2004), 207-220.   CrossRef
  3. Z. Chen and J. Huang: Global robust servomechanism problem of lower triangular systems in the general case. Systems Control Lett. 52 (2004), 209-220.   CrossRef
  4. Z. Chen and J. Huang: Dissipativity, stabilization, and regulation of cascade-connected systems. IEEE Trans. Automat. Control 49 (2004), 635-650.   CrossRef
  5. Z. Chen and J. Huang: Robust output regulation with nonlinear exosystems. Automatica 41 (2005), 1447-1454.   CrossRef
  6. H. Chen, W. Sun, Z. Sun and J. T. W. Yeow: Second order sliding mode control of a 2D torsional MEMS micromirror with sidewall electrodes. J. Micromech. Microengrg. 23 (2013), 1-9.   CrossRef
  7. J. Huang: Nonlinear Output Regulation: Theory and Applications. SIAM, Philadelphia 2004.   CrossRef
  8. J. Huang and Z. Chen: A general framework for tackling the output regulation problem. IEEE Trans. Automat. Control 49 (2004), 2203-2218.   CrossRef
  9. A. Isidori: Nonlinear Control Systems, Volume II. Springer-Verlag, New York 1999.   CrossRef
  10. Z. Jiang and I. Mareels: A small-gain control method for nonlinear cascaded systems with dynamic uncertainties. IEEE Trans. Automat. Control 42 (1997), 292-308.   CrossRef
  11. M. Krstić, I. Kanellakopoulos and P. Kokotović: Nonlinear and Adaptive Control Design. Wiley, New York 1995.   CrossRef
  12. L. Liu and J. Huang: Global robust stabilization of cascade-connected systems with dynamic uncertainties without knowing the control direction. IEEE Trans. Automat. Control 51 (2006), 1693-1699.   CrossRef
  13. L. Liu and J. Huang: Global robust output regulation of output feedback systems with unknown high-frequency gain sign. IEEE Trans. Automat. Control 51 (2006), 625-631.   CrossRef
  14. R. Marino and P. Tomei: Nonlinear Control Design. Prentice-Hall International, 1995.   CrossRef
  15. Y. Ma, S. Islam and Y. Pan: Electrostatic torsional micromirror with enhanced tilting angle using active control methods. IEEE Trans. Mechatronics 16 (2011), 635-650.   CrossRef
  16. R. D. Nussbaum: Some remaks on a conjecture in parameter adaptive control. Systems Control Lett. 3 (1983), 243-246.   CrossRef
  17. B. Rehák, S. Čelikovský, J. Ruiz and J. Orozco-Mora: A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem. Kybernetika 45 (2009), 427-444.   CrossRef
  18. E. D. Sontag and A. R. Teel: Changing supply functions in input/state stable systems. IEEE Trans. Automat. Control 40 (1995), 1476-1478.   CrossRef
  19. E. D. Sontag: Mathematical control theory. In Texts in Applied Mathematics: Vol. 6. Deterministic finite-dimensional systems (Second edition). Springer-Verlag, New York 1998.   CrossRef
  20. W. Sun, J. Huang and Z. Sun: Global robust stabilization for a class of time-varying output feedback systems. Internat. J. Robotics and Automation 26 (2011), 93-99.   CrossRef
  21. W. Sun, J. T. W. Yeow and Z. Sun: Robust adaptive control of a one degree of freedom electrostatic microelectromechanical systems model with output-error-constrained tracking. J. Control Theory Appl. 6 (2012), 111-119.   CrossRef
  22. W. Sun: Global robust output regulation of lower triangular systems with nonlinear exosystems and its application. J. Control Theory Appl. 11 (2013), 468-476.   CrossRef
  23. K. P. Tee, S. S. Ge and E. H. Tay: Barrier Lyapunov Functions for the control of output-constrained nonlinear systems. Automatica 45 (2009), 918-927.   CrossRef
  24. D. Xu and J. Huang: Robust adaptive control of a class of nonlinear systems and its applications. IEEE Trans. Circuits and Systems I: Regular Papers 57 (2010), 691-702.   CrossRef
  25. X. Yang and J. Huang: New results on robust output regulation of nonlinear systems with a nonlinear exosystem. Internat. J. Robust and Nonlinear Control 22 (2012), 1703-1719.   CrossRef
  26. X. Ye and J. Jiang: Adaptive nonlinear design without a priori knowledge of control. IEEE Trans. Automat. Control 43 (1998), 1617-1621.   CrossRef
  27. X. Ye: Decentralized adaptive stabilization of large-scale nonlinear time-delay systems with unknown high-frequency-gain signs. IEEE Trans. Automat. Control 56 (2011), 1473-1478.   CrossRef
  28. B. Zhang and W. Lan: Improving transient performance for output regulation problem of linear systems with input saturation. Internat. J. Robust and Nonlinear Control 23 (2013), 1087-1098.   CrossRef