Statistical machine-learning-based predictive control using barrier functions for process operational safety

Abstract

In this work, we present statistical model predictive control with Control Lyapunov-Barrier Functions (CLBF) built using machine learning approaches, and analyze closed-loop stability and safety properties in probability using statistical machine learning theory. A feedforward neural network (FNN) is used to construct the Control Barrier Function, and a generalization error bound can be obtained for this FNN via the Rademacher complexity method. The FNN Control Barrier Function is incorporated in a CLBF-based model predictive controller (MPC), which is used to control a nonlinear process subject to input constraints. The stability and safety properties of the closed-loop system under the sample-and-hold implementation of FNN-CLBF-MPC are evaluated in a statistical sense. We use a chemical process example to demonstrate the relation between various factors of building an FNN model and the generalization error, as well as the probabilities of closed-loop safety and stability for both bounded and unbounded unsafe sets.