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Non-linear control laws are disclosed and implemented with a controller and control system for maneuvering an underwater vehicle. The control laws change the phase of one Inferior-Olive (IO) neuron with respect to another IO. One control law is global, that is, the control law works (stable and convergent) for any initial condition. The remaining three control laws are local. The control laws are obtained by applying feedback linearization, while retaining non-linear characteristics. Each control law generates a profile (time history) of the control signal to produce a desired phase difference recognizable by a controller to respond to disturbances and to maneuver an underwater vehicle.