Global adaptive output feedback tracking for nonlinear systems linear in unmeasured states

A global adaptive output feedback dynamic compensator is proposed for stabilization and tracking of a class of systems that are globally diffeomorphic into systems in generalized output-feedback canonical form. This form includes as special cases the standard output-feedback canonical form and various other forms considered previously in the literature. Output-dependent nonlinearities are allowed to enter both additively and multiplicatively. The system is allowed to contain unknown parameters multiplying output-dependent nonlinearities. Under the assumption that a constant matrix can be found to achieve a certain property, it is shown that a reduced-order observer and a backstepping controller can be designed to achieve asymptotic tracking. It is also shown that this assumption can be removed by introducing extra dynamics. This represents the first adaptive output-feedback tracking results for this class of systems.

[1]  Laurent Praly,et al.  Output feedback asymptotic stabilization for triangular systems linear in the unmeasured state components , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

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

[3]  L. Praly,et al.  Stabilization by output feedback for systems with ISS inverse dynamics , 1993 .

[4]  P. Kokotovic,et al.  Nonlinear observers: a circle criterion design , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[5]  Ioannis Kanellakopoulos,et al.  Adaptive nonlinear observer/controller design for uncertain nonlinear systems 1 , 1999 .

[6]  P.V. Kokotovic,et al.  The joy of feedback: nonlinear and adaptive , 1992, IEEE Control Systems.

[7]  A. Isidori,et al.  Adaptive control of linearizable systems , 1989 .

[8]  H. Khalil.  Adaptive output feedback control of nonlinear systems represented by input-output models , 1996, IEEE Trans. Autom. Control..

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

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

[11]  A. Teel,et al.  Global stabilizability and observability imply semi-global stabilizability by output feedback , 1994 .

[12]  Gildas Besancon,et al.  State-Affine Systems and Observer-Based Control , 1998 .

[13]  Riccardo Marino,et al.  Nonlinear control design , 1995 .

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

[15]  M. Ikeda,et al.  Stabilization of Linear Systems , 1972 .

[16]  Petar V. Kokotovic,et al.  Tracking controllers for systems linear in the unmeasured states , 1995, Autom..

[17]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[18]  Zhong-Ping Jiang,et al.  Global output feedback tracking for nonlinear systems in generalized output-feedback canonical form , 2002, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[19]  Petar V. Kokotovic,et al.  Systematic design of adaptive controllers for feedback linearizable systems , 1991 .

[20]  A. Krener,et al.  Nonlinear observers with linearizable error dynamics , 1985 .

[21]  Zhong-Ping Jiang,et al.  Nonlinear observer/controller design for a class of nonlinear systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).