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Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs

Author

Listed:
  • Jasmina Djordjevic

    (University of Nis)

  • Sanja Konjik

    (University of Novi Sad)

  • Darko Mitrović

    (University of Vienna)

  • Andrej Novak

    (University of Zagreb)

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).

Suggested Citation

  • Jasmina Djordjevic & Sanja Konjik & Darko Mitrović & Andrej Novak, 2021. "Global Controllability for Quasilinear Nonnegative Definite System of ODEs and SDEs," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 316-338, July.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:1:d:10.1007_s10957-021-01886-z
    DOI: 10.1007/s10957-021-01886-z
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    References listed on IDEAS

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    1. Mao, Xuerong, 1995. "Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 281-292, August.
    2. Djordjević, Jasmina & Janković, Svetlana, 2015. "Backward stochastic Volterra integral equations with additive perturbations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 903-910.
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