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Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs

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Abstract

We consider exact and averaged control problem for a system of quasilinear ODEs and SDEs with a nonnegative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the function appearing in the nonlinear part of the system and then applying the Leray–Schauder fixed point theorem. We shall also need the continuous induction arguments to prolong the control to the final state which is a novel approach in the field. This enables us to obtain controllability for arbitrarily large initial data (so-called global controllability).

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Acknowledgements

This work is partially supported by Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. 451-03-9/2021-14/200125). It is also supported by the Lise Meitner Project Number M 2669-N32 of the Austrian Science Fund (FWF) and by the Croatian Science Foundation under Project MiTPDE (number IP-2018-01-2449). This article is based upon work from COST Action CA15225 FRACTIONAL and CA15125 DENORMS supported by COST (European Cooperation in Science and Technology). The permanent address of D.M. is University of Montenegro, Montenegro.

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Authors and Affiliations

  1. Faculty of Mathematics and Natural Sciences, University of Nis, Visegradska 33, 18000, Nis, Serbia

    Jasmina Djordjevic

  2. Faculty of Sciences, University of Novi Sad, Trg D.Obradovića 4, 21000, Novi Sad, Serbia

    Sanja Konjik

  3. Faculty of Mathematics, University of Vienna, Oskar Morgenstern Platz-1, 1090, Wien, Austria

    Darko Mitrović

  4. Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, Zagreb, Croatia

    Andrej Novak

Authors
  1. Jasmina Djordjevic
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  2. Sanja Konjik
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  3. Darko Mitrović
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  4. Andrej Novak
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Correspondence to Andrej Novak.

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Communicated by Firdaus E. Udwadia.

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Djordjevic, J., Konjik, S., Mitrović, D. et al. Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs. J Optim Theory Appl 190, 316–338 (2021). https://doi.org/10.1007/s10957-021-01886-z

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  • DOI: https://doi.org/10.1007/s10957-021-01886-z

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