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July 2018 Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise
Viorel Barbu, Michael Röckner, Deng Zhang
Ann. Probab. 46(4): 1957-1999 (July 2018). DOI: 10.1214/17-AOP1217

Abstract

We analyze the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrödinger 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.

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Viorel Barbu. Michael Röckner. Deng Zhang. "Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise." Ann. Probab. 46 (4) 1957 - 1999, July 2018. https://doi.org/10.1214/17-AOP1217

Information

Received: 1 July 2016; Revised: 1 July 2017; Published: July 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06919016
MathSciNet: MR3813983
Digital Object Identifier: 10.1214/17-AOP1217

Subjects:
Primary: 35J10 , 35Q40 , 49K20 , 60H15

Keywords: Backward stochastic equation , nonlinear Schrödinger equation , optimal control , Wiener process

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 4 • July 2018
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