Passivity, Small Feedback, and Synthesis of
Non-affine Systems in the Upper Triangular Form
Wei Lin
Warren E. Rupp Assistant Professor
Dept. of Electrical Engineering and Computer Science
Case Western Reserve University
This talk will present some recent advances in global asymptotic
stabilization (GAS)
of a significant class of non-affine control systems in the
upper-triangular form.
For an upper-triangular system which is
locally exponentially stabilizable and
encompasses the feedforward system and the challenging ball-and-beam
model,
we show how to construct a globally stabilizing, nested saturation
controller
with state-dependent saturation levels, using
a novel design approach which combines the nested saturation scheme
for marginally unstable linear systems
subject to input saturation (Teel, 1992), with the passivity-based
small feedback design technique (Lin, 1995 and 1996), developed for
global asymptotic stabilization of general non-affine
systems with marginally stable free dynamics.
For an upper-triangular system whose Jacobian linearization is not
controllable,
the nested saturation design does not work due to loss of the local
exponential stabilizability. In this situation we propose,
in contrast to the state-dependent nested saturation design,
a Lyapunov-based control scheme which provides a
bottom-up, step-by-step, recursive design procedure for the
construction
of a globally stabilizing controller whose magnitude is "small" in nature.
The proposed approach relies crucially on an effective coupling of
Mazenc-Praly's forwarding design (1996, 1997) and the passivity-based
small control strategy (Lin, 1995 and 1996).