Open AccessOptimal control and stabilization for linear continuous‐time mean‐field systems with delay
Author(s) -
Ma Xiao,
Qi Qingyuan,
Li Xun,
Zhang Huanshui
Publication year - 2022
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/cth2.12225
Subject(s) - observability , control theory (sociology) , algebraic riccati equation , mathematics , separation principle , optimal control , multiplicative function , controller (irrigation) , riccati equation , multiplicative noise , field (mathematics) , algebraic number , control (management) , mathematical optimization , computer science , differential equation , nonlinear system , mathematical analysis , signal transfer function , artificial intelligence , analog signal , state observer , biology , quantum mechanics , agronomy , digital signal processing , pure mathematics , computer hardware , physics
This paper studies optimal control and stabilization problems for continuous‐time mean‐field systems with input delay, which are the fundamental development of control and stabilization problems for mean‐field systems. There are two main contributions: (1) To the best of the authors' knowledge, the present paper is the first to establish the necessary and sufficient solvability condition for this kind of optimal control problem with input delay, and to derive the analytical form of an optimal controller through overcoming the obstacle that separation principle no longer holds for multiplicative‐noise systems. (2) For the stabilization problem, under the assumption of exact observability, it is strictly proven that the system is stabilizable if and only if the algebraic Riccati equation has a unique positive definite solution.