Branch and bound algorithm with applications to robust stability

Laleh Hosseini-Ravanbod (1) , Dominikus Noll (1) , Pierre Apkarian (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ONERA - The French Aerospace Lab [Toulouse]

We discuss a branch and bound algorithm for global optimization of NP-hard problems related to robust stability. This includes computing the distance to instability of a system with uncertain parameters, computing the minimum stability degree of a system over a given set of uncertain parameters, and computing the worst case H_\infty norm over a given parameter range. The success of our method hinges (1) on the use of an efficient local optimization technique to compute lower bounds fast and reliably, (2) a method with reduced conservatism to compute upper bounds, and (3) the way these elements are favorably combined in the algorithm.

Mots clés: NONSMOOTH OPTIMIZATION; MINIMUM STABILITY DEGREE; FREQUENCY DECOMPOSITION; BRANCH AND BOUND; DYNAMICAL SYSTEM; PARAMETRIC ROBUSTNESS; STABILITY MARGIN

Domaines: Algorithme et structure de données [cs.DS]

Laleh Hosseini-Ravanbod, Dominikus Noll, Pierre Apkarian. Branch and bound algorithm with applications to robust stability. Journal of Global Optimization, 2017, 67 (3), p. 553 - 579. ⟨10.1007/s10898-016-0424-6⟩. ⟨hal-01629180⟩