Nonregular feedback linearization: a nonsmooth approach

In this note, we address the problem of exact linearization via nonsmooth nonregular feedback. A criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs, and its application to nonholonomic systems is briefly discussed.

[1]  Shuzhi Sam Ge,et al.  Stabilization of underactuated mechanical systems: A non-regular back-stepping approach , 2001 .

[2]  Francis Clarke,et al.  Nonsmooth Analysis in Control Theory: A Survey , 2001, Eur. J. Control.

[3]  Einar Berglund,et al.  Control of an underwater vehicle with nonholonomic acceleration constraints , 1994 .

[4]  Xiaohua Xia,et al.  On Nonregular Feedback Linearization , 1997, Autom..

[5]  D. W. Bacon,et al.  A condition for dynamic feedback linearization of control-affine nonlinear systems , 1997 .

[6]  D Cheng,et al.  LINEARIZATION WITH DYNAMIC COMPENSATION , 1987 .

[7]  A. Krener On the Equivalence of Control Systems and the Linearization of Nonlinear Systems , 1973 .

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

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

[10]  Yun Ping Sun,et al.  Mixed H2/H cruise controller design for high speed train , 2001 .

[11]  Wei Huo,et al.  Exponential stabilization of non-holonomic systems: An ENI approach , 2001 .

[12]  I. Kolmanovsky,et al.  Switched mode feedback control laws for nonholonomic systems in extended power form , 1996 .

[13]  M. Branicky Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[14]  Roger W. Brockett,et al.  Feedback Invariants for Nonlinear Systems , 1978 .

[15]  Shuzhi Sam Ge,et al.  Nonregular feedback linearization for a class of second-order nonlinear systems , 2001, Autom..

[16]  Richard M. Murray,et al.  Steering nonholonomic systems in chained form , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[17]  Joao P. Hespanha,et al.  Logic-based switching control of a nonholonomic system with parametric modeling uncertainty , 1999 .

[18]  Philippe Martin,et al.  A Lie-Backlund approach to equivalence and flatness of nonlinear systems , 1999, IEEE Trans. Autom. Control..

[19]  J. Lévine,et al.  On dynamic feedback linearization , 1989 .

[20]  Daizhan Cheng,et al.  On p-normal form of nonlinear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[21]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[22]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[23]  A. Astolfi Discontinuous control of nonholonomic systems , 1996 .

[24]  S. Ge,et al.  Nonregular Feedback Linearization for a Class of Second-Order Systems with Application to Flexible Joint Robots , 2002 .

[25]  Wei Lin,et al.  On p-normal forms of nonlinear systems , 2003, IEEE Trans. Autom. Control..

[26]  Alessandro Astolfi,et al.  Discontinuous control of high-order generalized chained systems , 1999 .

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

[28]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[29]  R. Murray,et al.  Convergence Rates for Nonholonomic Systems in Power Form , 1993, 1993 American Control Conference.

[30]  Wei Lin,et al.  Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization , 2001 .