Finite-dimensional open-loop control generators for non-linear systems

This paper concerns itself with the existence of open-loop control generators for nonlinear (continuoustime) 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 nonsingular 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 nonlinear controllability notions. This version printed 10 July 1995. *To appear in Int.J.Control **Research supported in part by US Air Force Grant 0247