UDDAE_Optimization

MATLAB package UDDAE_Optimization: Stability optimization of uncertain time-delay systems. This eigenvalue-based stabilization method tunes the controller parameters (static or dynamic feedbacks) in order to improve the stability properties of a time-delay system, which can be affected by uncertainties, modeled by the realizations of a random vector. The closed-loop system is described by a delay differential algebraic equations (DDAE) of retarded type, in this way we can take into account integral controller and distributed terms. The time-delay system may non-linearly depend on the controller and uncertain parameters. In order to take into account the uncertainty, the stabilization minimizes an objective function consisting of the mean of the spectral abscissa with a variance penalty. For every realization of the uncertainties, the spectral abscissa (real part of the rightmost eigenvalue) is computed with the Infinitesimal Generator Approach, and then corrected with Newton’s method. The objective function and its gradient are numerically evaluated by computing integrals using quasi-Monte Carlo methods. The minimization of the objective function relies on the software HANSO (Hybrid Algorithm for Non Smooth Optimization).