LMIs in Control/Local Minimum of Polynomial via SOS Method

[UNDER CONSTRUCTION] - CME

The local minimum of a certain polynomial functions f(x) can be found using Sum-of-Squares (SOS) methods. Here we assume the local set has a P-Compact representation, and that this representation is used.

Required Data
A polynomial function f(x) whose minimum is desired.

A P-Compact representation of the set.

First Steps
Touch up on the Putinar Positivstellensatz and what it means for us.

Why does it work
Based in S-Procedure, with the Positivstellensatz all about the right representation.

Example
Code example in SOStools probably worthwhile!

Reference
SOS tools manual is a good one

Related LMIs
SOS Basics

Global Minimum