Approximated Explicit NMPC via Reinforcement Learning for Homomorphically Encrypted Process Control

This research proposes a novel approach to generating explicit, nearly-optimal (suboptimal) control policies in the form of neural networks with a structure that allows further mathematical operations within homomorphic encryption frameworks. The novelty of this paper also lies in presenting a reinforcement learning pathway to train the explicit control law without the necessity of prior model knowledge. A Deep Deterministic Policy Gradient algorithm is used to train the neural network, with the objective function adopted from nonlinear model predictive control. This paper presents a generalized methodology to train the control policy and evaluate it in a homomorphic encryption setup. Particular results are presented based on a software-in-the-loop simulation setup, where specifics like communication delays and computational overheads are considered.