Control and stabilization of nonholonomic dynamic systems

Abstract

A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested.<>