Fast Training of Neural Affine Models for Model Predictive Control: An Explicit Solution

Abstract

This work describes a nonlinear affine model developed especially for prediction in Model Predictive Control (MPC). A multi-model structure is used in which independent sub-models compute predictions for the consecutive sampling instants. All sub-models are affine with respect to the future values of the manipulated variable that are calculated in MPC. Model coefficients are time-varying; they are determined online by a neural network of the Radial Basis Function type. It is proved that the described model configuration makes it possible to formulate the training task as a least squares problem that has an explicit solution (the global optimum). A chemical reactor benchmark is considered to show advantages of the discussed modeling approach and the resulting MPC scheme. As a result of model affinity, MPC requires solving online simple quadratic optimization tasks.