Existence of Optimal Controls in the Absence of Cesari-Type Conditions forSemilinear Elliptic and Parabolic Systems

H. W. Lou
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H. W. Lou: Fudan University

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 2, No 7, 367-391

Abstract: Abstract Some new results on the existence of optimal controls are established for control systems governed by semilinear elliptic or parabolic equations. No Cesari type conditions are assumed. By proving existence theorems and analyzing the Pontryagin maximum principle for optimal relaxed state-control pairs for the corresponding relaxed problems, existence theorems of classical optimal pairs for the original problem are established. To treat the case of a noncompact control set, relaxed controls defined by finitely additive measures are used.

Keywords: Existence theorems; semilinear equations; optimal control; finitely additive measures; relaxed control (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1854-8

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