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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...
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,...
This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space , having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results...
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