  We establish three tractable, jointly sufficient conditions for the control
landscapes of non-linear control systems to be trap free comparable to those
now well known in quantum control. In particular, our results encompass
end-point control problems for a general class of non-linear control systems of
the form of a linear time invariant term with an additional state dependent
non-linear term. Trap free landscapes ensure that local optimization methods
(such as gradient ascent) can achieve monotonic convergence to effective
control schemes in both simulation and practice. Within a large class of
non-linear control problems, each of the three conditions is shown to hold for
all but a null set of cases. Furthermore, we establish a Lipschitz condition
for two of these assumptions; under specific circumstances, we explicitly find
the associated Lipschitz constants. A detailed numerical investigation using
the D-MOPRH control optimization algorithm is presented for a specific family
of systems which meet the conditions for possessing trap free control
landscapes. The results obtained confirm the trap free nature of the landscapes
of such systems.
