Mixed LQG and H_∞ coherent feedback control for linear quantum systems

ABSTRACT

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and H_∞ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as ‘coherent feedback controller’. A lower bound of the LQG control is proved. Then two different methods, rank-constrained linear matrix inequality method and genetic algorithm are for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier) demonstrate the effectiveness of these two proposed algorithms.

KEYWORDS:

• Coherent feedback control
• LQG control
• H_∞ control
• genetic algorithm
• rank-constrained LMI method

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported in part by National Natural Science Foundation of China (NSFC) [grant number 61374057] and Hong Kong RGC grants [grant number 531213] [grant number 15206915].