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Communication dans un congrès

A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n)

Abstract : For a right-invariant and controllable driftless system on SU(n), we consider a time-periodic reference trajectory along which the linearized control system generates su(n): such trajectories always exist and constitute the basic ingredient of Coron's return method. The open-loop controls that we propose, which rely on a left-invariant tracking error dynamics and on a fidelity-like Lyapunov function, are determined from a finite number of left-translations of the tracking error and they assure global asymptotic convergence towards the periodic reference trajectory. The role of these translations is to avoid being trapped in the critical region of this Lyapunov-like function. The convergence proof relies on a periodic version of LaSalle's invariance principle and the control values are determined by numerical integration of the dynamics of the system. Simulations illustrate the obtained controls for n = 4 and the generation of the C-NOT quantum gate.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-00474378
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Soumis le : lundi 19 avril 2010 - 19:14:31
Dernière modification le : jeudi 24 septembre 2020 - 17:04:18
Archivage à long terme le : : mardi 28 septembre 2010 - 12:07:13

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H.B. Silveira, P.S. Pereira da Silva, Pierre Rouchon. A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n). 48 th Conference on Decision and Control, 2009, Dec 2009, Shanghai, China. pp.363 - 368, ⟨10.1109/CDC.2009.5399811⟩. ⟨hal-00474378⟩

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