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Towards an example of a nonconvex monotone follower control problem

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Abstract

A one-dimensional monotone follower control problem with a nonconvex Lagrangian is considered. The control problem consists in tracking a standard Wiener process by an adapted nondecreasing process starting at 0. The verification theorem for the problem is presented. The optimal control and the value function are explicitly defined. For some values of parameters of the problem, it is shown that the value function belongs to C 2. An interesting feature of the optimally controlled state process is that for some initial states it has jumps at times other than the inital time.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Elizabeth City State University, Elizabeth City, NC, 27909, USA

    J. Luttamaguzi

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  1. J. Luttamaguzi
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.

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Luttamaguzi, J. Towards an example of a nonconvex monotone follower control problem. J Math Sci 161, 235–249 (2009). https://doi.org/10.1007/s10958-009-9549-1

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  • DOI: https://doi.org/10.1007/s10958-009-9549-1

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