Learning Nonlinear Reduced Order Models using State-Space Neural Networks with Ordered State Variance

TL;DR

This paper introduces a novel State-Space Neural Network with ordered variance for nonlinear reduced order modeling, demonstrating its effectiveness in system identification, control, and state estimation through simulations.

Contribution

It proposes the SSNNO architecture with ordered variance and a systematic model order reduction method, along with theoretical guarantees on prediction error bounds.

Findings

Effective nonlinear reduced order modeling demonstrated on a reactor process

Theoretical existence results for SSNNO with error bounds

Successful application in control and state estimation tasks

Abstract

A novel State-Space Neural Network with Ordered variance (SSNNO) is presented in which the state variables are ordered in decreasing variance. A systematic way of model order reduction with SSNNO is proposed, which leads to a Reduced order SSNNO (R-SSNNO). Theoretical results for the existence of an SSNNO with arbitrary bounds on the output prediction error are presented. The application of SSNNO in control: Model Predictive Control (MPC) and state estimation: Extended Kalman Filter (EKF) is discussed. The effectiveness of SSNNO in system identification and control is illustrated using simulations on a nonlinear continuous reactor process example.