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Description of the Attainable Sets of One-Dimensional Differential Inclusions

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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.

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Notes

  1. For more details about continuity of multivalued maps see [33].

  2. Observe that \(t\) is fixed and \(g\) is being evaluated at \(\underline{x}^*(t)\).

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Acknowledgments

This paper has been supported by Fondecyt-Chile through project 1120665, by Sao Paulo State Foundation—FAPESP-Brazil under Grants (11/01977-2, 11/13985-0, and 2013/07375-0) and by CNPq under Grant 309335/2012-4.

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Authors and Affiliations

  1. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    Yurilev Chalco-Cano

  2. UNESP - Univ. Estadual Paulista, Department of Applied Mathematics, Câmpus de São José do Rio Preto, R. Cristóvão Colombo 2265, Jd. Nazareth, São José do Rio Preto, SP , 15054-000, Brazil

    Valeriano A. de Oliveira & Geraldo N. Silva

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  1. Yurilev Chalco-Cano
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  2. Valeriano A. de Oliveira
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  3. Geraldo N. Silva
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Correspondence to Geraldo N. Silva.

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Chalco-Cano, Y., de Oliveira, V.A. & Silva, G.N. Description of the Attainable Sets of One-Dimensional Differential Inclusions. J Optim Theory Appl 164, 138–153 (2015). https://doi.org/10.1007/s10957-014-0563-1

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