Neural Network Augmented Model Predictive Control: Application to Active Brownian Particles

Model Predictive Control (MPC) is an effective algorithm that has been widely successful in various fields such as chemical processing and manufacturing. However, MPC is reliant on an accurate dynamic model to constrain the state dynamics in the optimal control problem. In practice, obtaining a high fidelity dynamical model is difficult and as the system changes over time, the model prediction accuracy worsens. Thus, we propose a data-driven method that combines MPC with Neural Network Augmented Models (NNAMs). NNAMs take partially known dynamics obtained from domain knowledge, e.g., mass or momentum balances, and approximate the unknown terms that are difficult to model with Neural Network (NNs). The NN parameters are estimated by solving a multi-step ahead prediction error minimization problem. This model is then used in MPC to control the system. We apply this method to control a partial differential equation describing the number density evolution of a large number of active Brownian particles under an actuated orienting field between two plates. A NNAM is used to model the number density which contains unknown terms corresponding to orientation states. We approximate the orientation states with a NN parameterized by the current number density and the recent history of number density and inputs. For a sequence of test inputs, our results show the NNAM number density prediction error is low. Thus, we use the NNAM with MPC for control and show that NNAM with MPC can achieve a similar stage costs compared to MPC with the full model.