Fault-Tolerant Control of Linear Quantum Stochastic Systems

In quantum engineering, faults may occur in a quantum control system, which will cause the quantum control system unstable or deteriorate other relevant performance of the system. This note presents an estimator-based fault-tolerant control design approach for a class of linear quantum stochastic systems subject to fault signals. In this approach, the fault signals and some commutative components of the quantum system observables are estimated, and a fault-tolerant controller is designed to compensate the effect of the fault signals. Numerical procedures are developed for controller design and an example is presented to demonstrate the proposed design approach.

[1]  M.R. James,et al.  $H^{\infty}$ Control of Linear Quantum Stochastic Systems , 2008, IEEE Transactions on Automatic Control.

[2]  John B. Moore,et al.  A Newton-like method for solving rank constrained linear matrix inequalities , 2006, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[3]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[4]  Guofeng Zhang,et al.  LQG/H∞ control of linear quantum stochastic systems , 2015, 2015 34th Chinese Control Conference (CCC).

[5]  M.R. James,et al.  Guaranteed Cost LQG Control of Uncertain Linear Stochastic Quantum Systems , 2007, 2007 American Control Conference.

[6]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[7]  Claudio Altafini,et al.  Modeling and Control of Quantum Systems: An Introduction , 2012, IEEE Transactions on Automatic Control.

[8]  Carsten W. Scherer,et al.  Multi-Objective Output-Feedback Control via LMI Optimization , 1996 .

[9]  Ian R. Petersen,et al.  Coherent quantum LQG control , 2007, Autom..

[10]  C. Scherer,et al.  Multiobjective output-feedback control via LMI optimization , 1997, IEEE Trans. Autom. Control..

[11]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[12]  Claus Kiefer,et al.  Quantum Measurement and Control , 2010 .

[13]  Ian R. Petersen,et al.  Fault tolerant quantum filtering and fault detection for quantum systems , 2015, Autom..

[14]  Aviziens.  Fault-Tolerant Systems , 1976, IEEE Transactions on Computers.

[15]  Ian R. Petersen,et al.  Quantum control theory and applications: A survey , 2009, IET Control Theory & Applications.

[16]  Hendra I. Nurdin,et al.  Network synthesis of mixed quantum-classical linear stochastic systems , 2011, 2011 Australian Control Conference.

[17]  N. Yamamoto.  Robust observer for uncertain linear quantum systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[18]  Hendra Ishwara Nurdin,et al.  Quantum Optical Realization of Classical Linear Stochastic Systems , 2013, Autom..

[19]  Hendra Ishwara Nurdin,et al.  Synthesis and structure of mixed quantum-classical linear systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[20]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[21]  A. Singh,et al.  Fault-tolerant systems , 1990, Computer.

[22]  M. V. Iordache,et al.  Diagnosis and Fault-Tolerant Control , 2007, IEEE Transactions on Automatic Control.

[23]  Barry W. Johnson.  Fault-Tolerant Microprocessor-Based Systems , 1984, IEEE Micro.

[24]  D. Lidar,et al.  Fault-tolerant quantum dynamical decoupling , 2004, 2005 Quantum Electronics and Laser Science Conference.

[25]  Matthew R. James,et al.  Quantum Dissipative Systems and Feedback Control Design by Interconnection , 2007, IEEE Transactions on Automatic Control.

[26]  Ian R. Petersen,et al.  Sliding mode control of two-level quantum systems , 2010, Autom..

[27]  Ian R. Petersen,et al.  Robust manipulation of superconducting qubits in the presence of fluctuations , 2014, Scientific Reports.