Robust control design of a class of nonlinear systems in polynomial lower-triangular form

This paper investigates the problem of global robust stabilization for a wide class of nonlinear systems, called polynomial lower-triangular form (pLTF), which expands LTF to a more general case. The aim is explicitly constructing the smooth controller for the class of systems with static uncertainties, by adding and modifying a power integrator in a recursive manner. The pLTF relaxes the restrictions on the structure of the normal LTF and enlarges the family of systems that are stabilizable. Examples are also provided to show the practical usage of this class of systems and the effectiveness of the design method.

[1]  John Tsinias,et al.  Triangular Systems: A Global Extension of the Coron-Praly Theorem on the Existence of Feedback-Integrator Stabilisers , 1997, Eur. J. Control.

[2]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework , 2002, IEEE Trans. Autom. Control..

[3]  Wei Lin,et al.  Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems , 2000 .

[4]  J. Coron,et al.  Adding an integrator for the stabilization problem , 1991 .

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

[6]  Dragan B. Dacic,et al.  A factorization approach to C/sup 1/ stabilization of nonlinear triangular systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[7]  H. Nijmeijer,et al.  Equivalence of nonlinear systems to triangular form: the singular case , 1996 .

[8]  John Tsinias,et al.  Sufficient lyapunov-like conditions for stabilization , 1989, Math. Control. Signals Syst..

[9]  Eduardo Aranda-Bricaire,et al.  Constructive nonsmooth stabilization of triangular systems , 1999 .

[10]  A. Isidori,et al.  New results and examples in nonlinear feedback stabilization , 1989 .

[11]  Wei Lin,et al.  Practical output tracking of nonlinear systems with uncontrollable unstable linearization , 2002, IEEE Trans. Autom. Control..

[12]  Alan S. I. Zinober,et al.  Nonlinear and Adaptive Control , 2003 .

[13]  Shuzhi Sam Ge,et al.  Adaptive NN control of uncertain nonlinear pure-feedback systems , 2002, Autom..

[14]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[15]  Wei Lin,et al.  Adaptive regulation of high-order lower-triangular systems : an adding a power integrator technique , 2000 .

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

[17]  A. Annaswamy,et al.  Adaptive control of nonlinear systems with a triangular structure , 1994, IEEE Trans. Autom. Control..

[18]  J. Tsinias,et al.  Explicit formulas of feedback stabilizers for a class of triangular systems with uncontrollable linearization , 1999 .