Machine learning-based input-augmented Koopman modeling and predictive control of nonlinear processes

TL;DR

This paper introduces an input-augmented Koopman modeling and predictive control method using deep neural networks to improve nonlinear process control, demonstrated through simulations on chemical and biological water treatment systems.

Contribution

It proposes a novel Koopman modeling approach with neural network-based lifting of states and inputs, enabling convex optimization-based iterative control for nonlinear processes.

Findings

Effective modeling of nonlinear systems with neural network-augmented Koopman approach

Successful application to chemical and biological water treatment processes

Demonstrated improved control performance and computational efficiency

Abstract

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original state-space to a lifted state space. In this work, we propose an input-augmented Koopman modeling and model predictive control approach. Both the states and the known inputs are lifted using two deep neural networks (DNNs), and a Koopman model with nonlinearity in inputs is trained within the higher-dimensional state-space. A Koopman-based model predictive control problem is formulated. To bypass non-convex optimization induced by the nonlinearity in the Koopman model, we further present an iterative implementation algorithm, which approximates the optimal control input via solving a convex optimization problem iteratively. The proposed method is applied to a chemical process and a biological water treatment process via simulations. The efficacy and advantages of the proposed modeling and control approach are demonstrated.