New Tools for Nonlinear Observer and Output-Feedback Design


Professor Murat Arcak


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.


Friday, November 8, 2002

3:30 – 4:30 p.m.

1500 EECS



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.