Open AccessMixed H 2 / H ∞ control for discrete‐time systems with input delay
Author(s) -
Li Xiaoqian,
Xu Juanjuan,
Wang Wei,
Zhang Huanshui
Publication year - 2018
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.2018.5486
Subject(s) - control theory (sociology) , uniqueness , stackelberg competition , control (management) , causality (physics) , state (computer science) , computer science , riccati equation , controller (irrigation) , mathematical optimization , mathematics , differential equation , algorithm , mathematical economics , mathematical analysis , physics , quantum mechanics , artificial intelligence , agronomy , biology
This study is concerned with the mixed H 2 / H ∞ control problem under an open‐loop information pattern with input delay. Compared with the delay‐free case, one of the main difficulties is the non‐causality caused by the time delay in the control input. The mixed H 2 / H ∞ control problem is reformulated as a leader–follower game and the Stackelberg strategy based on the maximum principle is introduced to deal with this. By introducing two co‐states to capture the future information and one new state to capture the past effects, the problem can be addressed. The controllers are designed by solving the symmetric and decoupled Riccati equations. Necessary and sufficient conditions that guarantee the existence and uniqueness of the solution are proposed in this study.