Abstract
In this paper, we consider a minimization problem of a cost functional associated to a nonlinear evolution feedback control system with a given boundary condition which includes the periodic one as a particular case. Specifically, by using an existence result for a system of inclusions involving noncompact operators (see Ref. 1), we first prove that the solution set of our problem is nonempty. Then, from the topological properties of this set, we derive the existence of a solution of the minimization problem under consideration.
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Communicated by R. Conti
This research was supported in part by the Research Project MURST (40%) “Teoria del Controllo dei Sistemi Dinamici” and by a CNR Bilateral Project. The authors are grateful to Prof. B. D. Gel'man for helpful discussions.
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Kamenskii, M.I., Nistri, P., Obukhovskii, V.V. et al. Optimal feedback control for a semilinear evolution equation. J Optim Theory Appl 82, 503–517 (1994). https://doi.org/10.1007/BF02192215
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DOI: https://doi.org/10.1007/BF02192215