Branch and bound algorithm with applications to robust stability |
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Authors: | Laleh Ravanbod Dominikus Noll Pierre Apkarian |
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Institution: | 1.Institut de Mathématiques,Université de Toulouse,Toulouse,France;2.Control System Department,ONERA,Toulouse,France |
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Abstract: | 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. |
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