A flat-zone modification for robust adaptive control of nonlinear output feedback systems with unknown high-frequency gains

This note deals with adaptive control of perturbed nonlinear output feedback systems with unknown high-frequency gains. The disturbances in the systems are assumed to be bounded, but the bounds are unknown. A flat-zone modification is proposed to incorporate both the bound estimation and Nussbaum gain design in the nonlinear adaptive control. To ensure the differentiability of stabilizing functions needed for backstepping design, high order terms are introduced in the Lyapunov function candidate with a flat zone around the neighborhood of the origin. The output tracking error converges to an arbitrarily small interval around zero.

[1]  Gang Feng,et al.  Analysis of a new algorithm for continuous-time robust adaptive control , 1999, IEEE Trans. Autom. Control..

[2]  Zhengtao Ding.  Adaptive asymptotic tracking of nonlinear output feedback systems under unknown bounded disturbances. , 1998 .

[3]  Xudong Ye,et al.  Adaptive nonlinear output-feedback control with unknown high-frequency gain sign , 2001, IEEE Trans. Autom. Control..

[4]  Iven M. Y. Mareels,et al.  Adaptive systems - an introduction , 1996, Systems and control.

[5]  Achim Ilchmann,et al.  High-gain adaptive control: an overview , 1996 .

[6]  Zhengtao Ding.  Robust adaptive control of nonlinear output-feedback systems under bounded disturbances , 1998 .

[7]  Zhengtao Ding,et al.  Almost disturbance decoupling of uncertain nonlinear output feedback systems , 1999 .

[8]  I. Kanellakopoulos,et al.  Adaptive nonlinear control without overparametrization , 1992 .

[9]  Eugene P. Ryan,et al.  Universal λ-tracking for nonlinearly-perturbed systems in the presence of noise , 1994, Autom..

[10]  Z. Ding.  Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high-frequency gains , 1998, IEEE Trans. Autom. Control..

[11]  K. Furuta,et al.  Improving the robustness of Nussbaum-type regulators by the use of σ-modification—local results , 1989 .

[12]  I. Kanellakopoulos,et al.  Systematic Design of Adaptive Controllers for Feedback Linearizable Systems , 1991, 1991 American Control Conference.

[13]  Miroslav Krstic,et al.  Nonlinear and adaptive control de-sign , 1995 .

[14]  R. Marino,et al.  Global adaptive output-feedback control of nonlinear systems. I. Linear parameterization , 1993, IEEE Trans. Autom. Control..

[15]  Gang Feng.  New robust model reference adaptive control algorithm , 1994 .

[16]  Achim Ilchmann,et al.  Non-Identifier-Based High-Gain Adaptive Control , 1993 .