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Robust Optimisation with Normal Vectors on Critical Manifolds of Disturbance-Induced Stability Loss

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Abstract

Dynamic systems that are subject to fast disturbances, parametrised by a disturbance vector d, undergo bifurcations for some values of the disturbance d. In this work we specifically examine those bifurcations which give rise to system trajectories that leave the domain of attraction of a desired system state. We derive equations which describe the manifold of bifurcation values (that is the manifold of disturbances d which cause the system trajectory to abandon the desired domain of attraction) and the corresponding normal vectors. The system of equations can then be used to find the smallest critical disturbance in physical, biological or other systems, or to robustly optimise design parameters of an engineered system.

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Authors and Affiliations

  1. AVT Prozesstechnik, RWTH Aachen University, Aachen, Germany

    Benedikt Wirth, Johannes Gerhard & Wolfgang Marquardt

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  1. Benedikt Wirth
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  2. Johannes Gerhard
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  3. Wolfgang Marquardt
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Correspondence to Benedikt Wirth.

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Communicated by G. Haller.

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Wirth, B., Gerhard, J. & Marquardt, W. Robust Optimisation with Normal Vectors on Critical Manifolds of Disturbance-Induced Stability Loss. J Nonlinear Sci 21, 57–92 (2011). https://doi.org/10.1007/s00332-010-9076-8

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  • DOI: https://doi.org/10.1007/s00332-010-9076-8

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