Colloidal self-assembly with Model Predictive Control

We propose a Model Predictive Control (MPC) method to facilitate self-assembly of a quadrupole colloidal system for defect-free two-dimensional crystals. A Langevin equation model is developed to model the thermodynamics of the colloidal system and provides predictions for optimization. A finite prediction horizon is used to optimize the input trajectory over different control horizons. The stochastic optimization problem is solved using simulated annealing, and simulation results of the optimized input trajectory demonstrate that the MPC algorithm proposed in this paper is able to accelerate the process of crystallization of our quadrupole colloidal system. Future work will focus on reducing the computational time and on experimental implementation.