This paper presents an original method, based on artificial neural networks, to reduce the torque ripple in a permanent-magnet non-sinusoidal synchronous motor. Solutions for calculating optimal currents are deduced from geometrical considerations and without a calculation step which is generally based on the Lagrange optimization. These optimal currents are obtained from two hyperplanes. The study takes into account the presence of harmonics in the back-EMF and the cogging torque. New control schemes are thus proposed to derive the optimal stator currents giving exactly the desired electromagnetic torque (or speed) and minimizing the ohmic losses. Either the torque or the speed control scheme, both integrate two neural blocks, one dedicated for optimal currents calculation and the other to ensure the generation of these currents via a voltage source inverter. Simulation and experimental results from a laboratory prototype are shown to confirm the validity of the proposed neural approach.