Optimal Design of a Colloidal Self-Assembly Process

An optimal feedback policy is designed for a stochastic colloidal assembly process using dynamic programming. Actuator-parameterized Langevin equations describe the system dynamics of an electric-field mediated assembly process, and are used to construct a discrete-state Markov chain model for input to the Markov decision process (MDP) framework. The state of the system is based on an order parameter representing the overall system configuration, as it transitions from a fluid to a crystalline state. The MDP-based optimal control policy is computed for both the finite- and infinite-horizon cases, with design goals based on maximizing crystallinity. Simulations show that the proposed MDP-based policies are able to drive the system rapidly to the desired high-crystallinity state, or to reach a desired tradeoff between high crystallinity and low control effort.