A Quantum Langevin Formulation of Risk-Sensitive Optimal Control

Abstract

In this paper we formulate a risk-sensitive optimal control problem for continuously monitored open quantum systems modelled by quantum Langevin equations. The optimal controller is expressed in terms of a modified conditional state, which we call a risk-sensitive state, that represents measurement knowledge tempered by the control purpose. One of the two components of the optimal controller is dynamic, a filter that computes the risk-sensitive state. The second component is an optimal control feedback function that is found by solving the dynamic programming equation. The optimal controller can be implemented using classical electronics. The ideas are illustrated using an example of feedback control of a two-level atom.

References in corpus (4)

• Quantum Continual Measurements and a Posteriori Collapse on CCR
• Risk-Sensitive Optimal Control of Quantum Systems
• Stochastic Schrodinger equations
• Bellman equations for optimal feedback control of qubit states

Cited by in corpus (8)

• A discrete invitation to quantum filtering and feedback control
• Conditional and unconditional Gaussian quantum dynamics
• Robust observer for uncertain linear quantum systems
• Quantum risk-sensitive estimation and robustness
• Quantum projection filter for a highly nonlinear model in cavity QED
• Quantum feedback for rapid state preparation in the presence of control imperfections
• Effects of time delay in feedback control of linear quantum systems
• A proposal of adaptive parameter tuning for robust stabilizing control of $N$--level quantum angular momentum systems