Electrical control of magnetism has been demonstrated in multiferroic compounds and ferromagnetic semiconductors, but electrical switching of a substantial net magnetization at room temperature has not been demonstrated in these materials. This goal has instead been achieved in heterostructures comprising ferromagnetic films in which electrically driven magnetic changes arise due to strain or exchange bias from ferroic substrates, or due to charge effects induced by a gate. However, previous work focused on electrical switching of an in-plane magnetization or involved the assistance of applied magnetic fields. In heterostructures made of juxtaposed ferroelectric and ferromagnetic layers, we have shown electrical control with no applied magnetic field of the perpendicular magnetization of small features [1] and of magnetic stripe domains patterns [2]. Here we investigate Ni81Fe19 films on ferroelectric substrates with and without buffer layers of Cu, whose presence precludes charge-mediated coupling. Ni81Fe19 has virtually zero magnetostriction, but sufficiently thin films show large magnetostriction, and thus, on increasing film thickness through the threshold for zero magnetostriction, we have seeked the crossover from charge- to strain-mediated coupling. We will then show that strain associated with the motion of 90°- ferroelectric domain walls in a BaTiO3 substrate, can switch the magnetization of an array of overlying single-domain Ni dots. [1] M. Ghidini, R. Pellicelli, J. L. Prieto, X. Moya, J. Soussi, J. Briscoe, S. Dunn and N. D. Mathur, Nature Communications 4 (2013) 1453. [2] M. Ghidini, F.Maccherozzi, X. Moya, L. C. Phillips, W.Yan, J. Soussi, N. Métallier, M.Vickers, , N. -J.Steinke, R. Mansell, C. H. W. Barnes, S. S. Dhesi, and N. D. Mathur, Adv. Mater.doi: 10.1002/adma.201404799 (2015).