Generalized Empirical Gramians for Trajectory Relevant Nonlinear Model Reduction

In this paper we present a generalization of empirical gramians as used for nonlinear model reduction. This approach enables us to directly use data, generated by relevant trajectories, to compute the empirical controllability gramian. The observability gramian can be derived along the trajectory while ensuring that the perturbed initial conditions remain feasible. The feasibility of the perturbed initial conditions was an issue has not been discussed in literature. The reduction method is demonstrated on a plant with reactor and distillation unit with a recycle and base control. The model represents dynamics of class of real processes an is therefore more relevant than a case study on one single unit operation.