Open AccessStandard solution to mixed H 2 / H ∞ control with regular Riccati equation
Author(s) -
Li Xiaoqian,
Xu Juanjuan,
Zhang Huanshui
Publication year - 2020
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/iet-cta.2020.0061
Subject(s) - riccati equation , mathematics , algebraic riccati equation , weighting , optimal control , norm (philosophy) , linear quadratic regulator , mathematical optimization , control theory (sociology) , control (management) , computer science , mathematical analysis , partial differential equation , artificial intelligence , medicine , political science , law , radiology
In this study, the authors are concerned with the long‐standing mixed H 2 / H ∞ problem for discrete linear systems. The main contribution is to derive the standard solution of the mixed H 2 / H ∞ problem by a regular Riccati equation. Firstly, in H ∞ ‐optimisation procedure, the optimal strategy ( u , w ) is explicitly given where the H ∞ ‐norm is maximised by w and H 2 ‐norm is minimised by u at the same time. It is noted that there exists an arbitrary item in the optimal strategy for the positive semi‐definite weighting matrices. Secondly, the H 2 ‐optimisation problem is explicitly solved with respect to the arbitrary item. Finally, the standard solution of the mixed H 2 / H ∞ problem is explicitly given in terms of regular Riccati equations by combining the optimal strategy ( u , w ) in H ∞ optimisation procedure and the optimal solution of H 2 optimisation procedure. Examples are presented to show the effectiveness of the proposed approach.