Open AccessComputing frequency response of non‐parametric uncertainty model of MIMO systems using υ‐gap metric optimization
Author(s) -
Tabibian Seyed Masoud,
Ataei Mohammad,
Koofigar Hamid Reza
Publication year - 2021
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/cth2.12110
Subject(s) - semidefinite programming , coprime integers , parametric statistics , convex optimization , metric (unit) , mathematical optimization , mathematics , linear matrix inequality , context (archaeology) , computation , optimization problem , control theory (sociology) , computer science , algorithm , regular polygon , paleontology , statistics , operations management , geometry , control (management) , artificial intelligence , biology , economics
This paper presents the computation of the non‐parametric uncertainty model for multi input multi output (MIMO) systems, which is described by normalized coprime factors (NCF) using the frequency response data of the system. This computation is accomplished by minimizing a υ‐gap metric criterion. For this purpose, the problem is formulated to a convex optimization context, such that a semidefinite programming (SDP) can be implemented. Minimization constraints and the normality constraints of coprime factors are converted to linear matrix inequalities (LMI). Thus, by convex optimization algorithms, the semidefinite programming will be optimized. The proposed method can also be used for non‐square multi input multi output systems in a conservative assumption. So, through the first process of optimization, the frequency responses of the normalized coprime factors are derived. Finally, to evaluate the performance of the proposed method in the computation of the normalized coprime factors of a system, the simulated results of this method are compared with those obtained by the other methods for two types of systems.