Set stabilization of nonholonomic chained form systems

Conventional controllers for the nonholonomic systems all stabilize the closed loop system to a target point. In this paper, considering the nonholonomic chained form system, a control design approach based on set stabilization idea is proposed. The proposed control laws can asymptotically stabilize the closed loop system to a set of given target points. First, for the first-order subsystem, a state feedback control law is designed to guarantee that the state of the closed loop system is asymptotically stabilized to a set of points. Second, for the n-1th order subsystem of other states, another state feedback control law is designed to guarantee that the states of the closed loop subsystem are asymptotically stabilized. Finally, an application example, the set stabilization of periodic target points, is given. Simulation results show the effectiveness of the method.

[1]  Yu-Ping Tian,et al.  Exponential stabilization of nonholonomic dynamic systems by smooth time-varying control , 2002, Autom..

[2]  Arjan van der Schaft,et al.  Proceedings of the 32nd IEEE Conference on Decision and Control, 1993 , 1993 .

[3]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[4]  Yu-Ping Tian,et al.  Set Stabilization of a Modified Chua's Circuit , 2005, Int. J. Bifurc. Chaos.

[5]  Jianqiang Yi,et al.  Smooth time-varying regulation of nonholonomic chained systems , 2004, ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, 2004..

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

[7]  A. Astolfi.  Discontinuous control of the Brockett integrator , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[8]  Shihua Li,et al.  Global set stabilization of the spacecraft attitude control problem based on quaternion , 2010 .

[9]  Cheng Daizhan.  Stabilization and Controllability of a Class of Nonholonomic Systems , 2002 .

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

[11]  Shihua Li,et al.  Set stabilization of Chua’s circuit via piece-wise linear feedbacks , 2005 .

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

[13]  David Angeli.  Almost global stabilization of the inverted pendulum via continuous state feedback , 2001, Autom..

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

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

[16]  Eduardo Sontag,et al.  Remarks on control Lyapunov functions for discontinuous stabilizing feedback , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[17]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[18]  Hirokazu Nishitani,et al.  Discontinuous control of nonholonomic systems using nondifferentiable Lyapunov functions , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[19]  Li Yu,et al.  An LMI approach to guaranteed cost control of linear uncertain time-delay systems , 1999, Autom..

[20]  Yiguang Hong,et al.  Stabilization of uncertain chained form systems within finite settling time , 2005, IEEE Transactions on Automatic Control.

[21]  S. Bhat,et al.  A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon , 2000 .

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