Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control

Abstract

We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.

14 pages, no figures (modified notation)

References in corpus (10)

• Quantum feedback control and classical control theory
• Feedback control of quantum state reduction
• Adaptive homodyne measurement of optical phase
• Quantum Continual Measurements and a Posteriori Collapse on CCR
• Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry
• Risk-Sensitive Optimal Control of Quantum Systems
• Stochastic Schrodinger equations
• Bellman equations for optimal feedback control of qubit states
• Quantum nonlinear dynamics of continuously measured systems
• Continuous measurement of canonical observables and limit Stochastic Schrodinger equations

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