Controllability of Nonlinear Sequential Networks

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Abstract
A sequential network is said to be controllable if there exists at least one integer k such that it is possible to transition between any pair of arbitrary states ( S α , S β ) in exactly k steps. In this paper, necessary and sufficient conditions are given for a nonlinear sequential network to be controllable. Strong connectedness is a necessary condition for controllability. It is shown that the existence of two cycles C 1 and C 2 on a strongly connected sequential network, whose cycle lengths L 1 and L 2 are relatively prime, is both necessary and sufficient for controllability. Simple test procedures are also developed which determine if a sequential network is controllable and which determine the transition sequences.

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