In this paper we prove that for two-input three-dimensional driftless analytic systems, there exists an open dense subset /spl Omega/ of the state space, whose complement is an analytic subset of positive codimension, such that for every point p/spl isin//spl Omega/ there exist a positive integer N and a neighborhood U of p with the property that every time-optimal trajectory an U is either a concatenation of bang and singular arcs with at most N pieces or replaceable by a bang-bang trajectory with at most two switchings.
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