Closed-loop training of static output feedback neural network controllers for large systems: A distillation case study

TL;DR

This work addresses the computational burden and state estimation requirements of MPC for large constrained systems by offline training a static output‑feedback neural policy in a closed loop via an optimise‑and‑learn framework. It incorporates measurement noise, allows selective use of measurements through elastic‑net regularisation, and demonstrates that a 50‑state nonlinear distillation column can be controlled effectively with a compact neural policy. The results show that a reduced set of measurements can yield robust performance close to an MPC baseline, with policy robustness improving when not relying on feedforward information from disturbances. The study highlights the trade-offs between full‑measurement performance, input sparsity, and resilience to model mismatch, offering practical guidance for deploying learned controllers in large-scale process systems.

Abstract

The online implementation of model predictive control for constrained multivariate systems has two main disadvantages: it requires an estimate of the entire model state and an optimisation problem must be solved online. These issues have typically been treated separately. This work proposes an integrated approach for the offline training of an output feedback neural network controller in closed loop. Online this neural network controller computers the plant inputs cheaply using noisy measurements. In addition, the controller can be trained to only make use of certain predefined measurements. Further, a heuristic approach is proposed to perform the automatic selection of important measurements. The proposed method is demonstrated by extensive simulations using a non-linear distillation column model of 50 states.

Figures (13)

• Figure 1: Sketch of a distillation column with LV-configuration and external flows shown.
• Figure 2: Disturbance profile used in the comparison of the control policies.
• Figure 3: Violin plot showing the temperature range of the distillation column subject to disturbances, to find the relevant operating region of the column.
• Figure 4: Temperature profiles of distillation column controlled by MPC with test disturbances. The dashed black lines indicate the pure component boiling points, and the red dash-dotted line indicates the temperature in the reboiler and condenser.
• Figure 5: Temperature profile using $\kappa_{all}$. Black dashed lines indicated $T_{bL}$ and $T_{bH}$, red dash-doted lines indicates $T_1$ and $T_{N_T}$, and the green lines indicate column temperatures.