Nonconvex Valid Uncertainty Modelling Approach for Robust Control Synthesis

This paper proposes an alternative nonconvex approach to fit single-input and single-output transfer function models on magnitude frequency-based response measurements, with additional constraints such as upper boundness, stability, minimum phase and validity with respect to provided data. The proposed solution presents an improvement over the established Log-Chebyshev convex fit which is used as a well-placed starting point and refines the optimization to become less conservative and feasible in cases where (near) singularities are present and limit its sole application. As such, our contribution provides advantages in cases such as in $\mu$-synthesis where the uncertainty model should have a low order to guarantee no conservativeness of the structured singular value approximation. Two case studies are described and discussed which show brought improvements.