Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations

• 成果类型: Article
• 署名作者: Aronna, M. Soledad; Bonnans, J. Frederic; Kroner, Axel
• 署名单位: Getulio Vargas Foundation; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; Universite Paris Saclay
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-016-1093-4
• 发表日期: 2018
• 页码: 717-757
• 关键词: 2nd-order analysis

摘要

In this paper we consider second order optimality conditions for a bilinear optimal control problem governed by a strongly continuous semigroup operator, the control entering linearly in the cost function. We derive first and second order optimality conditions, taking advantage of the Goh transform. We then apply the results to the heat and wave equations.