Nonlinear model prediction Jacobian approximation using state-independent order reduction

This paper presents a method for efficiently approximating the nonlinear model prediction Jacobian matrix using state-independent model order reduction. The predictive Jacobian matrix describes how changes in the predictive inputs affect the state prediction. This method aims to reduce computation time of nonlinear model predictive control of large-scale systems, typically with spatially distributed parameters. The approach employs a unique combination of step-wise linearization, order reduction, and time discretization to calculate predictive impulse responses, followed by the reduction inverse. The reduction transformation considered is agnostic to the current state, which contributes to saving computation time. A numerical example of continuous heating is included to demonstrate the efficiency and applicability of the method.