Developments in Time-Varying Feedback Stabilization of Nonlinear Systems

Abstract Over the last ten years, time-varying feedback has emerged as a new approach for the asymptotic stabilization of highly nonlinear control systems. This paper gives an overview of the developments made in this area. In particular, relations between theoretical developments and practical motivations are emphasized.

[1]  Pascal Morin,et al.  Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems Via Oscillatory Approximation of Lie Brackets in Closed Loop , 1999, SIAM J. Control. Optim..

[2]  Pascal Morin,et al.  Application of Backstepping Techniques to the Time-Varying Exponential Stabilisation of Chained Form Systems , 1997, Eur. J. Control.

[3]  Richard M. Murray,et al.  Nonholonomic control systems: from steering to stabilization with sinusoids , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[4]  Jean-Michel Coron,et al.  Stabilization of controllable systems , 1996 .

[5]  Zhong-Ping Jiang,et al.  Global stabilization of parametric chained-form systems by time-varying dynamic feedback , 1996 .

[6]  Karim Ait-Abderrahim,et al.  Feedback stabilization of a nonholonomic wheeled mobile robot , 1991, Proceedings IROS '91:IEEE/RSJ International Workshop on Intelligent Robots and Systems '91.

[7]  Jean-Michel Coron,et al.  Explicit feedbacks stabilizing the attitude of a rigid spacecraft with two control torques , 1996, Autom..

[8]  C. Samson.  Control of chained systems application to path following and time-varying point-stabilization of mobile robots , 1995, IEEE Trans. Autom. Control..

[9]  J. Coron,et al.  Smooth stabilizing time-varying control laws for a class of nonlinear systems. application to mobile robots , 1992 .

[10]  Zhong-Ping Jiang,et al.  Time-varying feedback stabilization of the attitude of a rigid spacecraft with two controls , 1994 .

[11]  Eduardo Sontag,et al.  Remarks on continuous feedback , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[12]  J. Coron.  On the stabilization in finite time of locally controllable systems by means of continuous time-vary , 1995 .

[13]  S. Shankar Sastry,et al.  Orientation control of the dynamic satellite , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[14]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[15]  Claude Samson,et al.  Velocity and torque feedback control of a nonholonomic cart , 1991 .

[16]  Kristin Y. Pettersen,et al.  Exponential Stabilization of an Underactuated Surface Vessel , 1997 .

[17]  Christopher I. Byrnes,et al.  On the attitude stabilization of rigid spacecraft , 1991, Autom..

[18]  Giuseppe Oriolo,et al.  Feedback control of a nonholonomic car-like robot , 1998 .

[19]  Pascal Morin,et al.  Control of nonlinear chained systems: from the Routh-Hurwitz stability criterion to time-varying exponential stabilizers , 2000, IEEE Trans. Autom. Control..

[20]  O. J. Sørdalen,et al.  Exponential stabilization of nonholonomic chained systems , 1995, IEEE Trans. Autom. Control..

[21]  Semyon Meerkov,et al.  Principle of vibrational control: Theory and applications , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[22]  Jean-Baptiste Pomet,et al.  Time-varying exponential stabilization of nonholonomic systems in power form , 1994 .

[23]  Claude Samson,et al.  Time-varying Feedback Stabilization of Car-like Wheeled Mobile Robots , 1993, Int. J. Robotics Res..

[24]  C. Samson,et al.  Time-varying exponential stabilization of a rigid spacecraft with two control torques , 1997, IEEE Trans. Autom. Control..

[25]  J. Lévine,et al.  Sufficient conditions for dynamic state feedback linearization , 1991 .

[26]  Zexiang Li,et al.  Smooth Time-Periodic Feedback Solutions for Nonholonomic Motion Planning , 1993 .

[27]  Claude Samson,et al.  Exponential Stabilization of Certain Configurations of the General N-Trailer System , 1998 .

[28]  O. J. Sordalen,et al.  Exponential stabilization of mobile robots with nonholonomic constraints , 1992 .

[29]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[30]  Gianna Stefani.  Polynomial approximations to control systems and local controllability , 1985, 1985 24th IEEE Conference on Decision and Control.

[31]  Henry Hermes,et al.  Nilpotent and High-Order Approximations of Vector Field Systems , 1991, SIAM Rev..

[32]  H. Sussmann.  Subanalytic sets and feedback control , 1979 .

[33]  Wensheng Liu,et al.  An Approximation Algorithm for Nonholonomic Systems , 1997 .

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

[35]  Alain Micaelli,et al.  Trajectory tracking for two-steering-wheels mobile robots , 1994 .

[36]  Pascal Morin,et al.  Robust Stabilisation of the Angular Velocity of a Rigid Body with Two Controls , 1996, Eur. J. Control.

[37]  A. Yu. Khapalov.  Optimal measurement trajectories for distributed parameter systems , 1992 .

[38]  Ole Jakob Sørdalen,et al.  Conversion of the kinematics of a car with n trailers into a chained form , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[39]  M. Kawski.  Stabilization of nonlinear systems in the plane , 1989 .

[40]  L. Rosier.  Homogeneous Lyapunov function for homogeneous continuous vector field , 1992 .

[41]  R. Murray,et al.  Exponential stabilization of driftless nonlinear control systems using homogeneous feedback , 1997, IEEE Trans. Autom. Control..