An Augmented Lagrangian Method for the Optimal H∞ Model Order Reduction Problem

Author:

Yang Hongli1ORCID,Zhao Maoxian1ORCID

Affiliation:

1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China

Abstract

This paper treats the computational method of the optimal H model order reduction (MOR) problem of linear time-invariant (LTI) systems. Optimal solution of MOR problem of LTI systems can be obtained by solving the LMIs feasibility coupling with a rank inequality constraint, which makes the solutions much harder to be obtained. In this paper, we show that the rank inequality constraint can be formulated as a linear rank function equality constraint. Properties of the linear rank function are discussed. We present an iterative algorithm based on augmented Lagrangian method by replacing the rank inequality with the linear rank function. Convergence analysis of the algorithm is given, which is distinct to the now available heuristic methods. Numerical experiments for the MOR problems of continuous LTI system illustrate the practicality of our method.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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