OPTIMAL BILINEAR CONTROL OF NONLINEAR STOCHASTIC SCHRTMDINGER EQUATIONS DRIVEN BY LINEAR MULTIPLICATIVE NOISE

• 成果类型: Article
• 署名作者: Barbu, Viorel; Roeckner, Michael; Zhang, Deng
• 署名单位: Romanian Academy; Alexandru Ioan Cuza University; University of Bielefeld; Shanghai Jiao Tong University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1217
• 发表日期: 2018
• 页码: 1957-1999
• 关键词: schrodinger-equations; lyapunov control; EXISTENCE

摘要

We analyze the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrodinger equation perturbed by a linear multiplicative Wiener process. The existence of an open-loop optimal control and first-order Lagrange optimality conditions are derived, via Skorohod's representation theorem, Ekeland's variational principle and the existence for the linearized dual backward stochastic equation. Moreover, our approach in particular applies to the deterministic case.