|
Overview |
|
My research has focused on the development of a general methodology for
designing control systems that meet accurate design specifications when
only partial information about the process is available. Measured data,
combined with the prior information, are to be used to develop a control
oriented model that is tailored towards these specifications. In practice,
iterative identification and control is inevitable, and a theory for performing
this iteration has been developed. Its main branches are robust control,
and control oriented system identification. My research is concentrated
on developing these two branches.
|
Robust Control |
|
In the area of robust control, I have developed a computational methodology
for designing controllers that meet accurate combined time-domain and frequency-domain
specifications in the presence of plant and input uncertainty which is
based on solving linear and convex optimization problems. This theory builds
on my previous work on the l1 theory which constitutes the building
block of this methodology. This methodology captures in a quantitative
and precise way the fundamental limitations of controller design in the
presence of uncertainty and provides a systematic tool for design. Matlab-based
CAD environment is currently under development that allows graphical interaction
with the software to analyze and design robust controllers. Many of the
fundamental ideas behind this has been summarized in the book: Control
of Uncertain Systems: A Linear Programming Approach, which I co-authored
with Ignacio Diaz-Bobillo. Recently, I have initiated a strong effort that
aims at generalizing and developing a parallel theory of robust control
for nonlinear systems.
|
Control Oriented System Identification |
|
Control oriented system identification differs from the traditional system
identification theory in that it requires a model and a deterministic description
of the unmodeled dynamics. The standard stochastic theory fails to provide
such information. As a consequence, I have developed a general deterministic
minimax theory that encompasses the stochastic theory as a special case,
and is entirely based on sample path deterministic analysis. As a result
of performing identification in this set up, one gets a model, a set description
of the unmodeled dynamics, and a possibility to tradeoff parametric and
nonparametric uncertainty in the description of the unmodeled dynamics.
A complete analysis of consistency and the sample complexity of this problem
has been performed for different classes of disturbance sets and conditions
on these sets have been derived to recover the results from the stochastic
formulation. These results will eventually lead to a complete complexity-based
theory for learning and adaptive control.
|
|
 |
