Model predictive control of non-interacting active Brownian particles

Active matter systems are strongly driven to assume non-equilibrium distributions owing to their self-propulsion, e.g., flocking and clustering. Controlling the active matter systems' spatiotemporal distributions offers exciting applications such as directed assembly, programmable materials, and microfluidic actuation. However, these applications involve environments with coupled dynamics and complex tasks, making intuitive control strategies insufficient. This necessitates the development of an automatic feedback control framework, where an algorithm determines appropriate actions based on the system's current state. In this work, we control the distribution of active Brownian particles by applying model predictive control (MPC), a model-based control algorithm that predicts future states and optimizes the control inputs to drive the system along a user-defined objective. The MPC model is based on the Smoluchowski equation with a self-propulsive convective term and an actuated spatiotemporal-varying external field that aligns particles with the applied direction, similar to a magnetic field. We apply the MPC framework to control a Brownian dynamics simulation of non-interacting active particles and illustrate the controller capabilities with two objectives: splitting and juggling sub-populations, and polar order flocking control. Model predictive control is used to guide the spatiotemporal distribution of active Brownian particles by forecasting future states and optimizing control inputs to achieve tasks like dividing a population into two groups.