Control of high-order nonholonomic systems in power chained form using discontinuous feedback

Addresses the problems of almost-asymptotic stabilization and global asymptotic regulation (GAR) for a class of high-order nonholonomic systems in power-chained form. This particular class of nonlinear systems is an extension of a nonholonomic system in chained form that has received considerable attention in the past few years. The nonholonomic system considered in this paper is not necessarily affine in the control variables and therefore cannot be handled by existing methods. Sufficient conditions are presented under which a discontinuous state-feedback control law (or a switching controller) can be recursively constructed, using the so-called "adding a power integrator" technique of C. Qian et al. (2001). We also illustrate how the results can be extend to multi-input systems in power-chained form. Simulation examples are provided to demonstrate the effectiveness of the proposed controllers.

[1]  Zhong-Ping Jiang,et al.  Iterative design of time-varying stabilizers for multi-input systems in chained form , 1996 .

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

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

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

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

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

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

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

[9]  P. Tsiotras,et al.  Control design for chained-form systems with bounded inputs , 2000 .

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

[11]  Alessandro Astolfi.  Asymptotic stabilization of nonholonomic systems with discontinuous control , 1995 .

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

[13]  A. Bloch,et al.  Control and stabilization of nonholonomic dynamic systems , 1992 .

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

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

[16]  Linda Bushnell,et al.  Stabilization of multiple input chained form control systems , 1995 .

[17]  Sergey V. Drakunov,et al.  Stabilization of Brockett's generalized canonical driftless system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[18]  Wei Lin.  Time-varying feedback control of nonaffine nonlinear systems without drift , 1996 .

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

[20]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[21]  P. Tsiotras,et al.  Exponentially convergent control laws for nonholonomic systems in power form 1 1 Supported in part b , 1998 .

[22]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .