Summary: Approximate Reduction of Dynamical Systems
Paulo Tabuada, Aaron D. Ames, Agung Julius and George Pappas
Abstract-- The reduction of dynamical systems has a rich
history, with many important applications related to stability,
control and verification. Reduction is typically performed in an
"exact" manner--as is the case with mechanical systems with
symmetry--which, unfortunately, limits the type of systems to
which it can be applied. The goal of this paper is to consider a
more general form of reduction, termed approximate reduction,
in order to extend the class of systems that can be reduced.
Using notions related to incremental stability, we give conditions
on when a dynamical system can be projected to a lower
dimensional space while providing hard bounds on the induced
errors, i.e., when it is behaviorally similar to a dynamical system
on a lower dimensional space. These concepts are illustrated
on a series of examples.
Modeling is an essential part of many engineering dis-
ciplines and often a key ingredient for successful designs.
Although it is widely recognized that models are only