Control of Heisenberg spin systems; Lie algebraic decompositions and action-angle variables
Vaidya, U.; Dapos;Alessandro, D.; Mezic, I.
Decision and Control, 2003. Proceedings. 42nd IEEE Conference on
Volume 4, Issue , 9-12 Dec. 2003 Page(s): 4174 - 4178 vol.4
Digital Object Identifier   10.1109/CDC.2003.1271804
Summary: In this paper, we consider the control of two coupled spin 1/2 particles that interact via Heisenberg interaction. We decompose the problem into a sequence of subproblems on a lower dimensional Lie group whose Lie algebra is the direct sum of su(2) and a two dimensional Abelian subalgebra. The associated lower dimensional control problems amount to controlling a two level system. To this aim, we derive a control algorithm which, from an energy function, calculates a nominal feedback law. The results guarantee convergence of the state from any initial condition to the desired final configuration.

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