Global Robust Stabilization of Minimum-Phase Nonlinear Systems with Uncertainty

The problem of global stabilization via state feedback is studied for a class of minimum-phase nonlinear systems with unknown unmodelled time-varying parameters or disturbances belonging to a given compact set. Sufficient conditions are presented for the existence of a robust stabilizing state-feedback controller. The controller is constructed explicitly by using a Lyapunov-based recursive design procedure. The proposed feedback control law is a smooth function of the state, and requires information of bounding functions on the size of uncertainties. In the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system, an adaptive controller is developed based on similar arguments, achieving global stability with state regulation. The main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics.

[1]  L. Fu,et al.  Output tracking control of nonlinear systems with mismatched uncertainties , 1992 .

[2]  Zhihua Qu,et al.  Robust Control of Nonlinear Uncertain Systems Under Generalized Matching Conditions , 1993, 1993 American Control Conference.

[3]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[4]  Wei Lin.  Global Robust Stabilization of Minimum-Phase Nonlinear Systems with Uncertainty , 1995 .

[5]  A. Isidori,et al.  Asymptotic stabilization of minimum phase nonlinear systems , 1991 .

[6]  Petar V. Kokotovic,et al.  Design of 'softer' robust nonlinear control laws , 1993, Autom..

[7]  Eduardo Sontag.  Further facts about input to state stabilization , 1990 .

[8]  J. Slotine,et al.  Robust input-output feedback linearization , 1993 .

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

[10]  David G. Taylor,et al.  Adaptive Regulation of Nonlinear Systems with Unmodeled Dynamics , 1988, 1988 American Control Conference.

[11]  Zhihua Qu,et al.  Robust control of cascaded and individually feedback linearizable nonlinear systems , 1994, Autom..

[12]  Riccardo Marino,et al.  Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, , 1993, Autom..

[13]  K. Nam,et al.  A model reference adaptive control scheme for pure-feedback nonlinear systems , 1988 .

[14]  A. Isidori.  Nonlinear Control Systems , 1985 .

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

[16]  R. Marino,et al.  Nonlinear H ∞ almost disturbance decoupling , 1994 .

[17]  Yuandan Lin,et al.  Recent results on Lyapunov-theoretic techniques for nonlinear stability , 1994, Proceedings of 1994 American Control Conference - ACC '94.

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

[19]  M. Corless,et al.  A new class of stabilizing controllers for uncertain dynamical systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[20]  George Leitmann,et al.  On ultimate boundedness control of uncertain systems in the absence of matching assumptions , 1982 .

[21]  Riccardo Marino,et al.  An extended direct scheme for robust adaptive nonlinear control , 1991, Autom..