H_{∞} and H_{2} controller design for linear systems is a difficult, nonconvex, nonsmooth
optimization problem when the order of the controller is fixed to be less than that of the open-loop plant, a typical
requirement in e.g. embedded aerospace control systems. In addition, it is often desired to compute a single controller which
stabilizes multiple plants simultaneously.

HIFOO is aimed at solving fixed-order stabilization and performance optimization problems. It depends on a hybrid algorithm for nonsmooth, nonconvex optimization based on quasi-Newton updating and gradient sampling. In particular, HIFOO address the following problems:

- fixed-order stabilization
- fixed-order strong stabilization
- fixed-order simultaneous stabilization
- fixed-order H
_{∞}optimization - fixed-order H
_{2}optimization - fixed-order complex stability radius optimization
- fixed-order stability margin (spectral abscissa) optimization
- fixed-order robust stability margin (pseudospectral abscissa) optimization

_{∞}performance of some plants subject to constraints on H

_{2}performance of other plants.

If you publish work that uses HIFOO, please refer to the following two papers:

- D. Arzelier, G. Deaconu, S. Gumussoy and D. Henrion.

H2 for HIFOO

International Conference on Control and Optimization with Industrial Applications, Bilkent University, Ankara, Turkey, August 2011

- S. Gumussoy, D. Henrion, M. Millstone and M.L. Overton.

Multiobjective Robust Control with HIFOO 2.0

Proceedings of the IFAC Symposium on Robust Control Design, Haifa, 2009

*HIFOO is based upon work supported by the National Science Foundation (NSF) under grants DMS-0714321, DMS-1016325 and DMS-1317205. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF.*