UDDAE_Optimization
swMATH ID:  38320 
Software Authors:  Fenzi, Luca; Michiels, Wim 
Description:  MATLAB package UDDAE_Optimization: Stability optimization of uncertain timedelay systems. This eigenvaluebased stabilization method tunes the controller parameters (static or dynamic feedbacks) in order to improve the stability properties of a timedelay system, which can be affected by uncertainties, modeled by the realizations of a random vector. The closedloop 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 timedelay system may nonlinearly 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 quasiMonte Carlo methods. The minimization of the objective function relies on the software HANSO (Hybrid Algorithm for Non Smooth Optimization). 
Homepage:  https://lucafe.github.io/Software.htm 
Dependencies:  Matlab 
Keywords:  eigenvalue analysis and optimization; delay differential algebraic equations of retarded type; uncertainty quantification; integrability of the spectral abscissa and its gradient 
Related Software:  HIFOO; IRAM; Matlab; PCA_SA; UQLab; Chebfun; nonlinear_pseudoabscissa; DDEBIFTOOL 
Referenced in:  3 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Robust stability optimization for linear delay systems in a probabilistic framework. Zbl 1362.65043 Fenzi, Luca; Michiels, Wim 
2017

Referenced by 4 Authors
3  Michiels, Wim 
2  Fenzi, Luca 
1  Meerbergen, Karl 
1  Ruymbeek, Koen 
Referenced in 3 Serials
1  Journal of Computational and Applied Mathematics 
1  Numerical Algorithms 
1  Linear Algebra and its Applications 
Referenced in 4 Fields
3  Numerical analysis (65XX) 
1  Linear and multilinear algebra; matrix theory (15XX) 
1  Probability theory and stochastic processes (60XX) 
1  Operations research, mathematical programming (90XX) 