Improved Model Order Reduction Techniques with Error Bounds

Abstract

Model Order Reduction (MOR) is a computational technique to build low order system from high order system by capturing the original properties of the actual system. The demand of MOR is ever higher during the study of dynamic behavior of the complex system. Because the complex high order systems impose difficulties e.g slow compu- tations and expensive storage requirements. So, MOR techniques facilitate to reduce these difficulties in order to provide fast computations and less storage requirements in the process of designing and simulation of large- scale physical systems. MOR capitu- lates Reduced Order Models (ROMs) which conserve the input output behavior of the original physical system. Construction of stable ROMs with low approximation error between original and compact (reduced) model is the main goal of MOR. MOR can be done in frequency-domain as well as in time-domain. Remarkable research work has been done on various directions of MOR to build ease in the designing, simulation and analysis of the complex dynamic systems. The precedent MOR techniques mostly have limitation of un-stability, large approximation error and lack of a priori error bounds in ROMs. Hence, the aim of this thesis is to construct improved model reduction tech- niques in order to overcome the existing problems of model reduction techniques in frequency domain. The proposed techniques guarantee the preservation of stability in ROM and low frequency-response approximation error with easily computable er- ror bound as compared to existing MOR techniques. In this thesis, firstly frequency weighted MOR problem is developed, then improved frequency weighted model re- duction techniques are proposed for continuous-time systems. A frequency limited vi Gramians-based MOR technique is also illustrated with error bounds for continuous-time systems. The applicability of the presented work is demonstrated in the context of some practical numerical examples to show the accuracy and efficacy of the proposed methods.