Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

ADAPTIVE STABILIZATION OF NON NECESSARILY INVERSELY STABLE CONTINUOUS-TIME SYSTEMS BY USING ESTIMATION MODIFICATION WITHOUT USING HYSTERESIS FUNCTION

  • Sen, M.De La (DEPARTAMENTO DE INGENIERIA DE SISTEMASY AUTOMATICA, FACULTAD DE CIENCIAS)
  • Published : 2001.02.01
Download PDF
⟨ Previous Next ⟩

Abstract

This note presents a an indirect adaptive control scheme for first-order continuous-time systems. The estimated plant model is controllable and then the adaptive scheme is free from singularities. The singularities are avoided through a modification of the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be nonsingular. That properties is achieved by ensuring that the absolute value of its determinant does not lie below a positive threshold. A modification scheme based on the achievement of a modified diagonally dominant Sylvester matrix of the parameter estimates is also given as an alternative method. This diagonal dominance is achieved through estimates modification as a way to guarantee the controllability of the modified estimated model when a controllability measure of the ‘a priori’ estimated model fails. In both schemes, the use of a hysteresis switching function for the modification of the estimates is not required to ensure the nonsingularity of the Sylvester matrix of the estimates.

Keywords

References

  1. IEEE Trans. Automat. Contr. v.AC-23 Adaptive control of single-input single-output linear systems A. Feuer;A.S.Morse
  2. IEEE Trans. Automat. Contr. v.AC-25 no.3 Global stability of parameter-adaptive control systems A.S.Morse
  3. IEEE Trans. Automat. Contr. v.AC-25 no.3 Stable adaptive controller design, Part Ⅱ:Proof of stability K.S. Narendra;Y.H.Lin;L.S.Valavani
  4. MCSS v.2 no.1 A state approach to the problem of adaptive control assignment R.D.Nussbaum
  5. Trans.Automat.Contr. v.AC-30 Adaptive stabilization of livear systems with unknown high frequency gains R.D.Mudgett;A.S.Morse
  6. IEEE Trans. Automat. Contr. v.AC-31 Stable adaptive regulation of arbitrary n-th order plants G.Kreisselmeier;M.C.Smith
  7. Int. J. of Control v.61 no.3 Adaptive control based on special compensation methods for time-varying systems subject to bounded disturbance V. Etxebarria;M. de la Sen
  8. Automatica v.20 On the stabilization condition in indirect adaptive control P. De Larminat
  9. IEEE Trans. Automat. Contr. v.AC-39 no.8 Adaptive stabilization of nonminimum phase first-order continuous-time systems R. Lozano;A.Osorio;J.Torres
  10. IEEE Trans. Automat. Contr. v.AC-39 no.1 Adaptive pole palcement without excitation probing signals R. Lozano;X. H. Zhao
  11. IEEE Trans. Automat. Control v.44 no.3 A note on the robust adaptive stabilization of a class of nominally first-order hybrid systems M. De la Sen
  12. Int. J. of Nonlinear Mechanics Robust adaptive stabilization of time-invariant first-order hybrid systems with covariance resetting
  13. IEEE Trans. Automat. Contr. v.AC-31 no.5 Stable discrete adaptive control with unknown high-frequency gain T.H.Lee;K.S.Narendra
  14. IEEE Trans. Automat. Contr. v.AC-31 Multirate hybrid adaptive control M. De la Sen
  15. IEEE Trans. Automat. Contr. v.33 no.1 Design issues in adaptive control R.Middleton;G.C.Goodwin;D.J.Hill.D.Q.Mayne
  16. Numerical Analysis Ⅰ v.CA D.Kincaid;W.Cheney
  17. Methods of Nonlinear Analysis Ⅰ v.61 R.Bellman
  18. Feedback Systems : Input Output Properties C.A.Desoer;M.Vidyasagar
  19. System Identification. Parameter and State Estimation P.Eykhoff
  20. Proceedings of the 34th Confeence on Decision and Control v.I A new algorithm for continuous - time robust adaptive control G. Feng