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

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.