New Tools for
Nonlinear Observer and Output-Feedback Design
Electrical, Computer
and Systems Engineering Department
Rensselaer
Polytechnic Institute
The first
part of the talk presents a new observer design for systems with a class of
multivariable nonlinearities. The approach is to represent the observer error
system as the interconnection of a linear block and a state-dependent feedback
nonlinearity. Convergence of the
estimates to the true states is then achieved under two restrictions which
allow the error system to satisfy the multivariable circle criterion: First, the nonlinearity must satisfy a
multivariable analog of the monotone nondecreasing property. Next, a linear
matrix inequality (LMI) must be feasible, which implies a positive real
property for the linear block. By further exploiting the structure of the
nonlinearity, we relax this second restriction with the help of a multiplier in
the LMI. The second part of the talk addresses how the new observer can be
incorporated in output-feedback design.
Unlike general nonlinear systems, where certainty-equivalence
implementation of a state-feedback controller may lead to instability, we prove
that a reduced-order variant of our observer design preserves global asymptotic
stability. We then present a small-gain redesign of the output-feedback
controller to achieve robustness against unmodeled dynamics. The observer and
output-feedback designs are illustrated with several physically motivated
examples.
3:30 – 4:30
p.m.
Biography:
Murat Arcak was born in Istanbul,
Turkey in 1973. He received the B.S. degree in Electrical and Electronics
Engineering from the Bogazici University, Istanbul, in 1996, and his M.S. and
Ph.D. degrees in Electrical and Computer Engineering from the University of
California, Santa Barbara, in 1997 and 2000, under the direction of Petar
Kokotovic. In 2001 he joined the Rensselaer Polytechnic Institute, Troy, NY, as
an assistant professor of
Electrical, Computer and Systems Engineering. His research interests are
in nonlinear control theory and applications. He is a member of IEEE and SIAM,
an associate editor on the Conference Editorial Board of IEEE Control Systems
Society, and serves as a consultant for United Technologies Research Center,
Hartford, CT.