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Explicit control laws for the periodic motion planning of controllable driftless systems on SU(n)

Abstract : In a previous work, the authors have introduced and treated the periodic motion planning problem for right-invariant driftless systems that evolve on SU(n), which in turn corresponds to an approximate motion planning control problem. Although the only assumption was the controllability of the system, the control laws are not explicitly known in general. By using analogous Lyapunov-like control techniques that were developed in that work, this paper complements its results and proves that if the system satisfies a more restrictive form of controllability, then the control laws are given by explicit and analytical expressions. Simulation results are presented for n = 4 and the generation of the C-NOT (Controlled-NOT) quantum logic gate.
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Submitted on : Tuesday, February 12, 2013 - 11:26:35 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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  • HAL Id : hal-00787793, version 1

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H.B. Silveira, P.S. Pereira da Silva, Pierre Rouchon. Explicit control laws for the periodic motion planning of controllable driftless systems on SU(n). Conference on Decision and Control (2012), Dec 2012, United States. pp.3640-3645. ⟨hal-00787793⟩

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