TITLE:
Combining Symbolic tools with interval analysis. An application to solve robust control problems.
AUTHORS:
Inès Ferrer-Mallorquí, Josep Vehí
KEYWORDS:
Symbolic computation, Interval analysis, Robust control
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.4 No.3,
May
16,
2014
ABSTRACT:
Complex systems are often subjected to uncertainties that make its model
difficult, if not impossible to obtain. A quantitative model may be inadequate
to represent the behavior of systems which require an explicit representation
of imprecision and uncertainty. Assuming that the uncertainties are structured,
these models can be handled with interval models in which the values of the
parameters are allowed to vary within numeric intervals. Robust control uses
such mathematical models to explicitly have uncertainty into account. Solving
robust control problems, like finding the robust stability or designing a
robust controller, involves hard symbolic and numeric computation. When
interval models are used, it also involves interval computation. The main
advantage using interval analysis is that it provides guaranteed solutions, but
as drawback its use requires the interaction with multiple kinds of data. We
present a methodology and a framework that combines symbolic and numeric
computation with interval analysis to solve robust control problems.