LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Local Minimum of Polynomial via SOS Method
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[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[edit | edit source]
A polynomial function f(x) whose minimum is desired.
A P-Compact representation of the set.
First Steps[edit | edit source]
Touch up on the Putinar Positivstellensatz and what it means for us.
Why does it work[edit | edit source]
Based in S-Procedure, with the Positivstellensatz all about the right representation.
Example[edit | edit source]
Code example in SOStools probably worthwhile!
Reference[edit | edit source]
SOS tools manual is a good one
Related LMIs[edit | edit source]
SOS Basics
Global Minimum