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Existence of optimal controls for some nonlinear processes

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Abstract

We prove the existence of optimal controls for an ordinary differential system which is nonlinear in the state functionx but is linear in the control functionu, that is,

$$dx/dt = f_1 (t,x) + f_2 (t,x)u$$

Rather weak regularity assumptions are made on the right-hand side of the above system, the constraints, and the cost functional.

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Authors and Affiliations

  1. FNRS, Institute of Mathematics, Free University of Brussels, Brussels, Belgium

    Jean-Pierre Gossez (Research Scientist)

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  1. Jean-Pierre Gossez
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Communicated by L. Cesari

This work was supported by FNRS, Brussels, Belgium.

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Gossez, JP. Existence of optimal controls for some nonlinear processes. J Optim Theory Appl 3, 89–97 (1969). https://doi.org/10.1007/BF00932459

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  • DOI: https://doi.org/10.1007/BF00932459

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