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

Control landscapes for a class of non-linear dynamical systems: sufficient conditions for the absence of traps