Markov decision process based time-varying optimal control for colloidal self-assembly

Crystals made of periodically well-ordered nano- and/or micro-scale elements can interact with light to give novel properties. These perfect crystals have applications in a wide range of areas. For example, invisibility cloaks that reroute light transmission make objects disappear. However, manufacturing such perfect crystals still remains challenging. Here, we propose a low-dimensional Markov decision process based dynamic programming framework to optimally control a colloidal self-assembly process for perfect crystal fabrication. Based on the simulation results, we demonstrate that an open-loop control policy identified with the proposed framework is able to reduce the defective assemblies from 46% of uncontrolled to 8% of controlled production. Moreover, when feedback is available, a closed-loop optimal finite-horizon control policy can further reduce the defective assemblies down to 5% out of 100 independent simulation runs.