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