Optimal coherent feedback control of linear quantum stochastic systems

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.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.

International Journal of ControlNov 15, 20167 citations

LINEAR QUANTUM STOCHASTIC CONTROL

Andreas Boukas

QP-PQ, quantum probability and white noise analysisJul 4, 19947 citations

Mixed LQG and $H_\infty$ Coherent Feedback Control for Linear Quantum SystemsMixed LQG and $H_\infty$ Coherent Feedback Control for Linear Quantum Systems

Cui, Lei, Zhiyuan Dong, Guofeng Zhang +1 more

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and $H_\infty$ 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 (LMI) method and genetic algorithm are proposed for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier, DPA) demonstrate the effectiveness of these two proposed algorithms.The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and $H_\infty$ 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 (LMI) method and genetic algorithm are proposed for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier, DPA) demonstrate the effectiveness of these two proposed algorithms.

arXiv:1611.04140Nov 13, 20160 citations

Optimal Probabilistic Quantum Control Theory

Randa Herzallah, Abdessamad Belfakir

arXiv:2210.16184Jan 1, 20220 citations

1 Direct and Indirect Couplings in Coherent Feedback Control of Linear Quantum Systems

Guofeng Zhang, M. R. James

The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.The purpose of this paper is to study and design direct and indirect couplings for use in coherent feedback control of a class of linear quantum stochastic systems. A general physical model for a nominal linear quantum system coupled directly and indirectly to external systems is presented. Fundamental properties of stability, dissipation, passivity, and gain for this class of linear quantum models are presented and characterized using complex Lyapunov equations and linear matrix inequalities (LMIs). Coherent $H^\infty$ and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.

Aug 16, 201699 citations

Mixed LQG and

H_\infty

Coherent Feedback Control for Linear Quantum Systems

The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and

H_\infty

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 (LMI) method and genetic algorithm are proposed for controller design. A passive system (cavity) and a non-passive one (degenerate parametric amplifier, DPA) demonstrate the effectiveness of these two proposed algorithms.

H^\infty

and LQG synthesis methods are extended to accommodate direct couplings using multistep optimization. Examples are given to illustrate the results.