MIT Department of Electrical Engineering & Computer Science

SPECIAL SEMINAR

Wednesday, March 22, 1995
Grier Room B, Room 34-401B

Refreshments at !:45 PM
Talk at 2:00 PM

Sets and Constraints as a Framework for Modeling and Control

Fernando Paganini
California Institute of Technology

Model uncertainty is the dominant issue in the performance of a control system. Successful mathematical methods for analysis and design have appeared, based on deterministic models for such uncertainties. Their main limitations are that they involve crude models of disturbance signals, and are not easily related to classical techniques for modeling and identification. Probabilistic methods are an alternative in these areas, but are not as adequate for system uncertainty.

In this talk we present a new formulation which provides a convenient meeting point of the stochastic and deterministic approaches; this metholodolgy is based on adding statistical signal constraints to a deterministic problem, which can then be solved with functional analytic tools. In particular, we present a complete solution to robust performance analysis subject to white-noise disturbances -- the Robust H2 problem.

More generally, we introduce a new framework for analysis of uncertain systems in implicit form. There is strong engineering motivation for implicit system representations, which are more closely related to modeling. Furthermore, this approach includes a general class of constrained analysis problems, and allows for a natural formulation of system identification questions.