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

Author

Xiaoting Wang ; Schirmer, S.G.

Author_Institution

Dept. of Appl. Math. & Theor. Phys., Univ. of Cambridge, Cambridge, UK

Volume

55

Issue

6

fYear

2010

fDate

6/1/2010 12:00:00 AM

Firstpage

1406

Lastpage

1411

Abstract

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.

Keywords

Lyapunov methods; asymptotic stability; bilinear systems; control system synthesis; position control; quantum theory; tracking; Hamiltonian criteria; Lyapunov control; asymptotic stability; dynamical system; quantum control theory; trajectory tracking problem; Asymptotic stability; Automatic control; Control design; Control systems; Control theory; Convergence; Lyapunov method; Quantum mechanics; Target tracking; Trajectory; Center manifolds; LaSalle invariance principle; Lyapunov control; quantum systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2042760

Filename

5409612