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We propose a deenition of \regular synthesis," more general than those suggested by other authors such as Boltyanskii and Brunovsk y, and an even more general notion of \regular presynthesis." We give a complete proof of the corresponding suuciency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline(More)
We propose a general strategy for solving the motion planning problem for real analytic, controllable systems without drift. The procedure starts by computing a control that steers the given initial point to the desired target point for an extended system, in which a number of Lie brackets of the system vector elds are added to the right-hand side. The main(More)
|{ We show that, for feedforward nets with a single hidden layer, a single output node, and a \transfer function" Tanhs, the net is uniquely determined by its input-output map, up to an obvious nite group of symmetries (permutations of the hidden nodes, and changing the sign of all the weights associated to a particular hidden node), provided that the net(More)