Model Boundary Approximation Method as a Unifying Framework for Balanced Truncation and Singular Perturbation Approximation

Abstract

We show that two widely accepted model reduction techniques, balanced truncation (BT) and balanced singular perturbation approximation (BSPA), can be derived as limiting approximations of a carefully constructed parameterization of linear time invariant systems by employing the model boundary approximation method (MBAM) [1]. We also show that MBAM provides a novel way to interpolate between BT and BSPA, by exploring the set of approximations on the boundary of the “model manifold,” which is associated with the specific choice of model parameterization and initial condition and is embedded in a sample space of measured outputs, between the elements that correspond to the two model reduction techniques. This paper suggests similar types of approximations may be obtainable in topologically similar places (i.e., on certain boundaries) on the associated model manifold of nonlinear systems if analogous parameterizations can be achieved, therefore extending these widely accepted model reduction techniques to nonlinear systems.1