Modeling in the Physical Domain: An Optimization-Based Approach

Abstract

With the increasing complexity of dynamic systems, model reduction has become an attractive research topic. A very useful type of reduced models is obtained by removing as many physical components as possible from the original model, known as model reduction in the physical domain. Many results have been achieved in this area during past decades. Nonetheless, the newest developments in engineering practice as well as in theoretical research have brought about further challenges and opportunities. This paper expands the scope of model reduction in physical domain, and proposes a criterion based on the H∞ norm of certain error model is proposed. The model reduction problem is then formulated as an optimization problem with bilinear matrix inequality (BMI) constraints, which can be solved with various processes. Several examples are presented to illustrate the use of the proposed model reduction scheme.