Time optimal cyclic crystallization

A time optimal cyclic control scheme for shape manipulation of multivariate crystal populations involving sequences of subsequent growth and dissolution phases is proposed in this note. Such strategies employ the unequal growth and dissolution rates for attaining morphologies that do not result directly from a pure growth or dissolution phase only. We prove that minimum time trajectories can be constructed by means of convex programs resulting in globally optimal bimodal control policies with piecewise constant supersaturation.