Digital control through finite feedback discretizability

State feedback and diffeomorphism on a given nonlinear plant to get finitely discretizable dynamics are used as a first step of a digital design procedure. Links with nilpotent and nilpotentizable Lie algebras are pointed out. The effectiveness of the control procedure is demonstrated on the basis of a case study.

[1]  H. Hermes,et al.  Nilpotent bases for distributions and control systems , 1984 .

[2]  S. Monaco,et al.  On the sampling of a linear analytic control system , 1985, 1985 24th IEEE Conference on Decision and Control.

[3]  H. Hermes Nilpotent approximations of control systems and distributions , 1986 .

[4]  Henry Hermes,et al.  Distributions and the Lie algebras their bases can generate , 1989 .

[5]  Gerardo Lafferriere,et al.  Motion planning for controllable systems without drift , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[6]  H. Sussmann,et al.  Local controllability and motion planning for some classes of systems with drift , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[7]  H. Sussmann,et al.  Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[8]  S. Monaco,et al.  Multirate Sampling and Zero Dynamics: from linear to nonlinear , 1991 .

[9]  M. Fliess,et al.  On Differentially Flat Nonlinear Systems , 1992 .

[10]  D. Normand-Cyrot,et al.  An introduction to motion planning under multirate digital control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[11]  Philippe Martin,et al.  On Differentially Flat Nonlinear Systems , 1992 .

[12]  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.

[13]  A. Chelouah,et al.  Digital control of nonholonomic systems two case studies , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[14]  M. Fliess,et al.  Flatness, motion planning and trailer systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[15]  R. Murray,et al.  Applications and extensions of Goursat normal form to control of nonlinear systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[17]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

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

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