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