Least squares and marginal log-likelihood model predictive control using normalizing flows

Journal of Process Control, vol. 156, pp. 103593

Abstract

Real-world (bio)chemical processes often exhibit stochastic dynamics with non-trivial correlations and state-dependent fluctuations. Model predictive control (MPC) often must consider these fluctuations to achieve reliable performance. However, most process models simply add stationary noise terms to a deterministic prediction. This work proposes using conditional normalizing flows as discrete-time models to learn stochastic dynamics. Normalizing flows learn the probability density function (PDF) of the states explicitly, given prior states and control inputs. In addition to standard least squares (LSQ) objectives, this work derives a marginal log-likelihood (MLL) objective based on the explicit PDF and Markov chain simulations. In a reactor study, the normalizing flow MPC setpoint errors in open and closed-loop cases are competitive with a full model-based stochastic MPC. Furthermore, the chance constraints lead to fewer constraint violations than the benchmark controller. The MLL objective yields slightly more stable optimization results than the LSQ, particularly for small scenario sets. • Multivariate probabilistic regression using normalizing flows. • Modeling of stochastic dynamics and state-dependent noise. • Marginal log-likelihood objective for model predictive control.

Authors 1

1. Eike Cramer corresponding Aachen

   RWTH Aachen University · University College London

   Affiliation as printed

   RWTH Aachen University, Process Systems Engineering (AVT.SVT), Aachen 52074, Germany

   University College London, Department of Chemical Engineering, London WC1E 7JE, United Kingdom