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Optimal control problems for a class of nonlinear evolution equations

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Abstract

In this paper we study optimal control problems for systems governed by nonlinear evolution equations. First we develop an existence theory for systems with a priori feedback using the reduction technique and a convexity-type hypothesis involving property Q. In doing this we also establish the nonemptiness of the set of admissible state-control pairs, by solving a nonlinear evolution inclusion. Then we obtain necessary conditions for optimality for a class of problems with terminal cost criterion and initial condition which is not a priori given but is only required to belong to a given set (systems with insufficient data in the terminology of Lions).

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, Athens, 157 80, Greece

    Nikolaos Halidias & Nikolaos S. Papageorgiou

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  1. Nikolaos Halidias
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  2. Nikolaos S. Papageorgiou
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Halidias, N., Papageorgiou, N.S. Optimal control problems for a class of nonlinear evolution equations. Periodica Mathematica Hungarica 45, 43–63 (2002). https://doi.org/10.1023/A:1022393812748

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