LMIs in Control/Click here to continue/Applications of Non-Linear Systems/Chebyshev Polynomials
Jump to navigation
Jump to search
Chebyshev Polynomials[edit | edit source]
Required data[edit | edit source]
A univariate Polynomial whose SOSINEQ range specification is desired
The Problem[edit | edit source]
Let be a univariate polynomial of degree being the coefficient of .
, subject to:
.
Formulation[edit | edit source]
The absolute value constraint can be easily rewritten using two inequalities, namely:
.
Solution[edit | edit source]
The optimal solution is , with being the n-th Chebyshev polynomial of the first kind.
Example[edit | edit source]
Code example in SOStools probably worthwhile!
Reference[edit | edit source]
SOS tools manual: https://sums-of-squares.github.io/sos/
Related LMIs[edit | edit source]
SOS Basics