Risk-Sensitive Optimal Control of Quantum Systems

The importance of feedback control is being increasingly appreciated in quantum physics and applications. This paper describes the use of optimal control methods in the design of quantum feedback control systems, and in particular the paper formulates and solves a risk-sensitive optimal control problem. The resulting risk-sensitive optimal control is given in terms of a new unnormalized conditional state, whose dynamics include the cost function used to specify the performance objective. The risk-sensitive conditional dynamic equation describes the evolution of our {\em knowledge} of the quantum system tempered by our {\em purpose} for the controlled quantum system. Robustness properties of risk-sensitive controllers are discussed, and an example is provided.