Time-limited H2-optimal model order reduction of linear systems with quadratic outputs

Abstract

Abstract

An important class of dynamical systems with several practical applications is that of linear systems with quadratic outputs. In time-limited model order reduction, the main goal is to ensure that the reduced-order model preserves the output response of the original system over a specified limited time range. To quantify the error within the specified time interval, this paper derives a mathematical expression for the time-limited H2-norm of linear systems with quadratic outputs, serving as a measure of the reduced model's accuracy over this period. Subsequently, the necessary conditions for achieving a local optimum of the time-limited H2 norm error are derived. The inherent inability to satisfy these optimality conditions within the Petrov-Galerkin projection framework is also discussed. An iterative fixed-point iteration algorithm based on these optimality conditions is proposed that ensures high fidelity within the desired time interval. Efficient implementation of the proposed algorithm for large-scale problems is also discussed. The efficacy of the proposed algorithm is demonstrated through two benchmark numerical examples. The results show that the proposed algorithm achieves higher accuracy than time-limited balanced truncation, as measured by the time-limited H2 norm error.