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On Reachability Analysis of Nonlinear Systems with Joint Integral Constraints

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Large-Scale Scientific Computing (LSSC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10665))

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Abstract

The problems of reachability for linear control systems with joint integral constraints on the state and input functions have been studied in the literature on the theory of set-valued state estimation. In this paper we consider a reachability problem for a nonlinear affine-control system on a finite time interval. The constraints on the state and control variables are given by the joint integral inequality, which assumed to be quadratic in the control variables. Assuming the controllability of the linearized system, we prove that any admissible control, that steers the control system to the boundary of its reachable set, is a local solution to an optimal control problem with integral cost functional.

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Acknowledgments

The research is supported by Russian Science Foundation, project № 16-11-10146.

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Authors and Affiliations

  1. N.N. Krasovskii Institute of Mathematics and Mechanics, S. Kovalevskaya str., 16, 620990, Ekaterinburg, Russia

    Mikhail Gusev

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  1. Mikhail Gusev
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Correspondence to Mikhail Gusev .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Lirkov

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

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Gusev, M. (2018). On Reachability Analysis of Nonlinear Systems with Joint Integral Constraints. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2017. Lecture Notes in Computer Science(), vol 10665. Springer, Cham. https://doi.org/10.1007/978-3-319-73441-5_23

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  • DOI: https://doi.org/10.1007/978-3-319-73441-5_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73440-8

  • Online ISBN: 978-3-319-73441-5

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