Nonlinear control and Lie-Backlund transformations: towards a new differential geometric standpoint

Abstract

Nonlinear control is related to Lie-Backlund transformation of some infinite-dimensional manifolds. State-variable representations, feedback and, especially, dynamic feedback linearization, i.e., flatness, are briefly examined, as well as the relationship with the differential algebraic approach. This setting provides a most natural framework for time scalings. We indicate via the carlike robot how to utilize this new time for stabilizing around a trajectory a driftless flat system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>