Abstract
Recurrent neural networks (RNNs) have been widely used to model nonlinear dynamic systems using time-series data. While the training error of neural networks can be rendered sufficiently small in many cases, there is a lack of a general framework to guide construction and determine the generalization accuracy of RNN models to be used in model predictive control systems. In this work, we employ statistical machine learning theory to develop a methodological framework of generalization error bounds for RNNs. The RNN models are then utilized to predict state evolution in model predictive controllers (MPC), under which closed-loop stability is established in a probabilistic manner. A nonlinear chemical process example is used to investigate the impact of training sample size, RNN depth, width, and input time length on the generalization error, along with the analyses of probabilistic closed-loop stability through the closed-loop simulations under Lyapunov-based MPC.
Highlights
Modeling large-scale, complex nonlinear processes has been a long-standing research problem in process systems engineering
In this work, we develop the methodological framework of generalization error bounds from machine learning theory for the development and verification of Recurrent neural networks (RNNs) models with specific theoretical accuracy guarantees and integrate these models into model predictive control system design for nonlinear chemical processes
We developed a generalization probabilistic error bound for RNN models by taking advantage of the Rademacher complexity method for vector-valued functions
Summary
Modeling large-scale, complex nonlinear processes has been a long-standing research problem in process systems engineering. Generalization error bound is a common methodology in statistical machine learning for evaluating the predictive performance of machine learning algorithms [33] This bound depends on a number of factors such as the number of data samples, the number of layers and neurons, bounds of weight matrices, initialization method, among others. In this work, we develop the methodological framework of generalization error bounds from machine learning theory for the development and verification of RNN models with specific theoretical accuracy guarantees and integrate these models into model predictive control system design for nonlinear chemical processes. Closed-loop simulations are carried out to analyze the probabilistic closed-loop stability and performance
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
