Coherent feedback $H^\infty$ control of quantum linear systems
This work addresses the robust and optimal control problem for quantum optical and optomechanical systems, providing a significant simplification over existing methods, though it is incremental in nature.
The paper tackles the coherent feedback H∞ control problem for linear quantum systems by introducing a simplified design methodology that ensures closed-loop stability and disturbance attenuation, reducing the computational requirement from solving two coupled algebraic Riccati equations to at most four Lyapunov equations. It demonstrates effectiveness on quantum optical devices like an empty optical cavity and a degenerate parametric amplifier, offering a computationally efficient procedure for robust control.
The purpose of this paper is to investigate the coherent feedback $H^\infty$ control problem for linear quantum systems. A key contribution is a simplified design methodology that guarantees closed-loop stability and a prescribed level of disturbance attenuation. It is shown that for general linear quantum systems, a physically realizable quantum controller can be obtained by solving at most four Lyapunov equations. In the passive case, a necessary and sufficient condition is provided in terms of two uncoupled pairs of Lyapunov equations. These results represent a significant simplification over the standard approach, which requires solving two coupled algebraic Riccati equations. The effectiveness of the proposed method is demonstrated through two typical quantum optical devices: an empty optical cavity and a degenerate parametric amplifier. These results provide a computationally efficient procedure for the robust and optimal control of quantum optical and optomechanical systems.