language: en

Switching through Singularities

C. J. Tomlin and S. S. Sastry
Department of Electrical Engineering and Computer Sciences University of California,
Berkeley CA 94720
{clairet, sastry}@eecs.berkeley.edu

Abstract Asymptotic tracking is studied for systems in which the relative degree is not well defined, meaning that the control law derived from exact input-output linearization has singularities in the state space. We propose a tracking control law which switches between approximate tracking [1] close to the singularities, and exact tracking away from the singularities, and we study the applicability of this law based on the behavior of the system's zero dynamics at the switching boundary. As in [1], the ball and beam example is used to motivate the study.

Keywords: Switching, nonlinear control, zero dynamics, exact and asymptotic tracking, nonminimum phase.

1 Introduction