Data driven stability analysis of black-box switched linear systems.

Kenanian, Joris;Balkan, Ayca;Jungers, Raphaël;Tabuada, Paulo
(2019) Automatica — Vol. 109 (2019)

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Authors
  • Kenanian, JorisDepartment of Electrical and Computer Engineering at University of California, Los Angeles (UCLA)
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  • Balkan, AycaDepartment of Electrical and Computer Engineering at University of California, Los Angeles (UCLA)
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  • Jungers, RaphaëlUCLouvain
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  • Tabuada, PauloDepartment of Electrical and Computer Engineering at University of California, Los Angeles (UCLA)
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Abstract
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius
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Kenanian, J., Balkan, A., Jungers, R., & Tabuada, P. (2019). Data driven stability analysis of black-box switched linear systems. Automatica, 109. https://doi.org/10.1016/j.automatica.2019.108533 (Original work published 2019)