Parameter Reduction for Stable Dynamical Systems based on Hankel Singular Values and Sensitivity Analysis

This paper addresses the problem of reducing insignificant or redundant information in parameter sets associated with fundamental models of dynamical systems. Whilst these parameters are important for describing physical or chemical relationships between the process variables, some of them only provide a marginal contribution to the input-output behavior of the system. Consequently, the identification of the latter parameters is difficult on the basis of recorded process data. Since this important issue has not attracted considerable attention over the past decade, the paper introduces and evaluates three techniques to assess the importance of each parameter to the overall input/output description of the process under study. The three presented methodologies include (1) parameter reduction where the contribution is measured by Hankel singular values, (2) reduction of the parameter space via singular value decomposition, and (3) a combination of the two techniques, where the number of parameters is reduced in a first step followed by reduction of the parameter space of the remaining parameters. The techniques are first developed for linear systems and an extension to nonlinear models is presented. The three techniques are compared using two case studies, one of which is a benchmark example from the nonlinear control literature.