Analysis of Effectiveness of Lyapunov Control for Non-Generic Quantum States

A Lyapunov-based control design for natural trajectory- tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for stationary target states subject to certain conditions on th...

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Veröffentlicht in:	IEEE transactions on automatic control 2010-06, Vol.55 (6), p.1406-1411
Hauptverfasser:	Xiaoting Wang, Schirmer, Sophie G
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Asymptotic properties Asymptotic stability Automatic control Center manifolds Computer science control theory systems Control design Control system synthesis Control systems Control theory Control theory. Systems Convergence Design engineering Dynamical systems Exact sciences and technology LaSalle invariance principle Lyapunov control Lyapunov method Quantum mechanics quantum systems Stability Target tracking Tracking problem Trajectory
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Zusammenfassung:	A Lyapunov-based control design for natural trajectory- tracking problems is analyzed for quantum states where the analysis in the generic case is not applicable. Using dynamical systems tools we show almost global asymptotic stability for stationary target states subject to certain conditions on the Hamiltonians, and discuss effectiveness of the design when these conditions are not satisfied. For pseudo-pure target states the effectiveness of the design is studied further for both stationary and non-stationary states using alternative tools.
ISSN:	0018-9286 1558-2523
DOI:	10.1109/TAC.2010.2042760