Abstract
This paper concerns itself with the existence of open-loop control generators for non-linear (continuous-time) systems. The main result is that, under relatively mild assumptions on the original system, and for each fixed compact subset of the state space, there always exists one such generator. This is a new system with the property that the controls it produces are sufficiently rich to preserve complete controllability along non-singular trajectories. General results are also given on the continuity and differentiability of the input-to-state mapping for various p-norms on controls, as well as a comparison of various non-linear controllability notions.
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