Advances in Optimisation and Machine Learning for Process Systems Engineering

Abstract

Optimisation is a valuable tool in process systems engineering, and has been widely used in design, control, process identification and many other areas. This thesis proposes novel applications of optimisation, as well as methods to solve optimisation problems efficiently and reliably. Recurring topics are the use of machine learning to reduce online computational effort, model predictive control, and optimisation under uncertainty. This thesis is a collation of research outputs and is divided in two parts: i) application driven works; ii) theory and algorithm driven works. The application driven research comprises of three works. The first focuses on training an output-feedback neural network control policy for a distillation column in closed-loop. This is a large problem and is particularly interesting because the control policies can be trained to only use a few measurements along the column. The second work demonstrates a model predictive control formulation for optimal inventory allocation, with the key aspect of the formulation being that we do not require accurate economic modelling or disturbance forecasting. The third work proposes a optimisation formulation for PID tuning in the frequency domain and solves it as a semi-infinite program. This formulation is a natural way to specify controller robustness and noise attenuation. The theoretical and algorithmic part of the thesis consists of four works. The first two aim to reduce the online computational demand of model predictive control by moving most of the demand offline. In the first of these a convex terminal cost is learned to allow the use of a one-step horizon, whilst in the second a method is proposed for closed-loop optimisation of neural network control policies under uncertainty. The third study demonstrates how multiple shooting can be used to improve the reliability of training neural networks embedded in differential equations. Lastly, the final work focuses on the development of improved lower bounding algorithms for the global optimisation of nonconvex semi-infinite programs. The key contributions of this thesis are the works on training neural network control policies in closed loop. Under mild conditions the proposed formulations enables trained policies to approximate model predictive control laws. However, the methodology is not restrictive and permits flexible design of controllers that can handle uncertainty and directly use measurements as feedback in a manner that cannot be done with traditional model predictive control.