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Description of the Attainable Sets of One-Dimensional Differential Inclusions

Author

Listed:
  • Yurilev Chalco-Cano

    (Universidad de Tarapacá)

  • Valeriano A. Oliveira

    (UNESP - Univ. Estadual Paulista, Department of Applied Mathematics)

  • Geraldo N. Silva

    (UNESP - Univ. Estadual Paulista, Department of Applied Mathematics)

Abstract

The role played by the attainable set of a differential inclusion, in the study of dynamic control systems and fuzzy differential equations, is widely acknowledged. A procedure for estimating the attainable set is rather complicated compared to the numerical methods for differential equations. This article addresses an alternative approach, based on an optimal control tool, to obtain a description of the attainable sets of differential inclusions. In particular, we obtain an exact delineation of the attainable set for a large class of nonlinear differential inclusions.

Suggested Citation

  • Yurilev Chalco-Cano & Valeriano A. Oliveira & Geraldo N. Silva, 2015. "Description of the Attainable Sets of One-Dimensional Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 138-153, January.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:1:d:10.1007_s10957-014-0563-1
    DOI: 10.1007/s10957-014-0563-1
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    References listed on IDEAS

    as
    1. Abbasbandy, S. & Nieto, Juan J. & Alavi, M., 2005. "Tuning of reachable set in one dimensional fuzzy differential inclusions," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1337-1341.
    2. A. B. Kurzhanski & P. Varaiya, 2001. "Dynamic Optimization for Reachability Problems," Journal of Optimization Theory and Applications, Springer, vol. 108(2), pages 227-251, February.
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