Reference
Abstract
We present abstraction techniques that transform a given non-linear dynamical system into a linear system, such that, invariant properties of the resulting linear abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change of bases transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction.
Furthermore, we present a technique to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding a linear system abstraction exists. If so, our technique yields the resulting abstract linear system, as well. This approach is further extended to search for a change of bases transformation that abstracts a given non-linear system into a system of linear differential inclusions. Our techniques enable the use of analysis techniques for linear systems to infer invariants for non-linear systems. We present preliminary evidence of the practical feasibility of our ideas using a prototype implementation.
BibTeX
@string{HSCC = "International Conference on Hybrid Systems: Computation and Control (HSCC)"}
@inproceedings{linearization-hscc11,
author = {Sriram Sankaranarayanan},
title = { Automatic Abstraction of Non-Linear Systems Using Change of Variables Transformations },
booktitle = HSCC,
year = {2011},
}