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Reachable Sets of Nonlinear Control Systems: Estimation Approaches

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Large-Scale Scientific Computing (LSSC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11958))

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Abstract

The dynamical control systems of a special structure with a combined nonlinearity of quadratic and bilinear kinds presenting in state velocities are studied. The uncertainty in initial states and in system parameters is also assumed and it has a set-membership type when only the bounding sets for unknown items are given. The ellipsoidal estimates of reachable sets are derived using the special structure of studied control system. The techniques of generalized solutions of Hamilton-Jacobi-Bellman (HJB) equations and HJB inequalities together with previously established results of ellipsoidal calculus are applied to find the set-valued estimates of reachable sets as the level sets of a related cost functional. The computational algorithms and related numerical examples are also given.

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Authors and Affiliations

  1. Department of Optimal Control, Krasovskii Institute of Mathematics and Mechanics, Russian Academy of Sciences, 16 S. Kovalevskaya Street, Ekaterinburg, 620108, Russian Federation

    Tatiana F. Filippova

  2. Ural Federal University, 19 Mira street, Ekaterinburg, 620002, Russian Federation

    Tatiana F. Filippova

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  1. Tatiana F. Filippova
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Correspondence to Tatiana F. Filippova .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Filippova, T.F. (2020). Reachable Sets of Nonlinear Control Systems: Estimation Approaches. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2019. Lecture Notes in Computer Science(), vol 11958. Springer, Cham. https://doi.org/10.1007/978-3-030-41032-2_58

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  • DOI: https://doi.org/10.1007/978-3-030-41032-2_58

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