Trajectory generation for quantum systems based on Lyapounov techniques

Mazyar Mirrahimi; Pierre Rouchon

doi:10.1016/S1474-6670(17)31238-7

Trajectory generation for quantum systems based on Lyapounov techniques

Mazyar Mirrahimi
, Pierre Rouchon

Mines ParisTech

Research output: Contribution to journal › Conference article › peer-review

Abstract

The convergence of a Lyapounov based control of the Schrodinger equation (finite dimensional) is analyzed via Lasalle invariance principle. When the linear tangent approximation around the goal eigen-state is controllable, such a feedback ensures global asymptotic convergence. When this linear tangent system is not controllable, the stability of the closed-loop system is not asymptotic. To overcome such lack of convergence we propose a modification based on adiabatic invariance. Simulations illustrate the simplicity and also the interest of these Lyapounov based controls for trajectory generation. Such control methods can also be adapted to tracking.

Original language	English
Pages (from-to)	291-296
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	37
Issue number	13
DOIs	https://doi.org/10.1016/S1474-6670(17)31238-7
Publication status	Published - 1 Jan 2004
Externally published	Yes
Event	6th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2004 - Stuttgart, Germany Duration: 1 Sept 2004 → 3 Sept 2004

Keywords

Adiabatic invariant
Control lyapounov function
Lasalle's invariant set
Nonlinear systems
Quantum systems

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10.1016/S1474-6670(17)31238-7

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title = "Trajectory generation for quantum systems based on Lyapounov techniques",

abstract = "The convergence of a Lyapounov based control of the Schrodinger equation (finite dimensional) is analyzed via Lasalle invariance principle. When the linear tangent approximation around the goal eigen-state is controllable, such a feedback ensures global asymptotic convergence. When this linear tangent system is not controllable, the stability of the closed-loop system is not asymptotic. To overcome such lack of convergence we propose a modification based on adiabatic invariance. Simulations illustrate the simplicity and also the interest of these Lyapounov based controls for trajectory generation. Such control methods can also be adapted to tracking.",

keywords = "Adiabatic invariant, Control lyapounov function, Lasalle's invariant set, Nonlinear systems, Quantum systems",

author = "Mazyar Mirrahimi and Pierre Rouchon",

note = "Publisher Copyright: Copyright {\textcopyright} 2004 IFAC.; 6th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2004 ; Conference date: 01-09-2004 Through 03-09-2004",

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doi = "10.1016/S1474-6670(17)31238-7",

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T1 - Trajectory generation for quantum systems based on Lyapounov techniques

AU - Mirrahimi, Mazyar

AU - Rouchon, Pierre

PY - 2004/1/1

Y1 - 2004/1/1

N2 - The convergence of a Lyapounov based control of the Schrodinger equation (finite dimensional) is analyzed via Lasalle invariance principle. When the linear tangent approximation around the goal eigen-state is controllable, such a feedback ensures global asymptotic convergence. When this linear tangent system is not controllable, the stability of the closed-loop system is not asymptotic. To overcome such lack of convergence we propose a modification based on adiabatic invariance. Simulations illustrate the simplicity and also the interest of these Lyapounov based controls for trajectory generation. Such control methods can also be adapted to tracking.

AB - The convergence of a Lyapounov based control of the Schrodinger equation (finite dimensional) is analyzed via Lasalle invariance principle. When the linear tangent approximation around the goal eigen-state is controllable, such a feedback ensures global asymptotic convergence. When this linear tangent system is not controllable, the stability of the closed-loop system is not asymptotic. To overcome such lack of convergence we propose a modification based on adiabatic invariance. Simulations illustrate the simplicity and also the interest of these Lyapounov based controls for trajectory generation. Such control methods can also be adapted to tracking.

KW - Adiabatic invariant

KW - Control lyapounov function

KW - Lasalle's invariant set

KW - Nonlinear systems

KW - Quantum systems

UR - https://www.scopus.com/pages/publications/77953083617

U2 - 10.1016/S1474-6670(17)31238-7

DO - 10.1016/S1474-6670(17)31238-7

M3 - Conference article

AN - SCOPUS:77953083617

SN - 2405-8963

VL - 37

SP - 291

EP - 296

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 13

T2 - 6th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2004

Y2 - 1 September 2004 through 3 September 2004

ER -

Trajectory generation for quantum systems based on Lyapounov techniques

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Keywords

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