In this paper, a finite horizon H∞control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon H∞control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon H∞control problem for an equivalent stochastic H∞control problem using some results from a corresponding deterministic problem following a dynamic game approach.In this paper, a finite horizon H∞control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon H∞control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon H∞control problem for an equivalent stochastic H∞control problem using some results from a corresponding deterministic problem following a dynamic game approach.

Proceedings of the ... American Control Conference/Proceedings of the American Control ConferenceJun 1, 20115 citations

On Some Model Problems in Quantum Control

Navin Khaneja

Control and manipulation of quantum mechanical systems using electromagnetic fields is a widely studied subject in areas of physics and chemistry, including spectroscopy, atomic molecular, and optical physics, and quantum chemistry.This article attempts to provide a glimpse into the rich class of bilinear control systems that are ubiquitous in these problems.In this article, we use control of spin systems in magnetic resonance as a model system to highlight characteristic feature of problems in quantum control.Background information is provided to enable the reader to appreciate new results and developments, where principled use of ideas from control theory have provided new insights into finding optimal ways to control and manipulate quantum mechanical systems.The study of deterministic and stochastic models that arise in problems in measurement and manipulation of quantum mechanical systems may foster new developments in control.Control and manipulation of quantum mechanical systems using electromagnetic fields is a widely studied subject in areas of physics and chemistry, including spectroscopy, atomic molecular, and optical physics, and quantum chemistry.This article attempts to provide a glimpse into the rich class of bilinear control systems that are ubiquitous in these problems.In this article, we use control of spin systems in magnetic resonance as a model system to highlight characteristic feature of problems in quantum control.Background information is provided to enable the reader to appreciate new results and developments, where principled use of ideas from control theory have provided new insights into finding optimal ways to control and manipulate quantum mechanical systems.The study of deterministic and stochastic models that arise in problems in measurement and manipulation of quantum mechanical systems may foster new developments in control.

Communications in Information and SystemsJan 1, 20099 citations

Control of quantum systems

G. Huang

Mar 1, 198013 citations

Finite Horizon $H^\infty$ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game ApproachFinite Horizon $H^\infty$ Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach

Aline I. Maalouf, Ian R. Petersen

In this paper, a finite horizon $H^\infty$ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon $H^\infty$ control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon $H^\infty$ control problem for an equivalent stochastic $H^\infty$ control problem following a dynamic game approach.In this paper, a finite horizon $H^\infty$ control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon $H^\infty$ control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon $H^\infty$ control problem for an equivalent stochastic $H^\infty$ control problem following a dynamic game approach.

SIAM Journal on Control and OptimizationJan 1, 20144 citations

CONTROL OF QUANTUM SYSTEMS

J. W. Clark, Dennis G. Lucarelli, Tzyh‐Jong Tarn

Recent Progress in Many-Body TheoriesDec 1, 20023 citations

Finite Horizon

H^\infty

Control for a Class of Linear Quantum Measurement Delayed Systems: A Dynamic Game Approach

In this paper, a finite horizon

H^\infty

control problem is solved for a class of linear quantum systems using a dynamic game approach for the case of delayed measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, the finite horizon

H^\infty

control problem for the class of linear quantum systems under consideration is solved for the case of delayed measurements by solving the finite horizon

H^\infty

control problem for an equivalent stochastic

H^\infty

control problem following a dynamic game approach.