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Mixed H 2 / H ∞ control of synchronization for coupled partial differential systems
Author(s) -
Wu KaiNing,
Wang Jian
Publication year - 2016
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3722
Subject(s) - synchronization (alternating current) , observer (physics) , control theory (sociology) , mathematics , differential (mechanical device) , partial differential equation , riccati equation , computer science , control (management) , mathematical analysis , topology (electrical circuits) , physics , combinatorics , quantum mechanics , artificial intelligence , thermodynamics
Summary In this paper, we address the mixed H 2 / H ∞ synchronization control for the coupled partial differential systems. First, we introduce the synchronization error dynamics and transform the problem of mixed H 2 / H ∞ synchronization control of coupled partial differential systems into the problem of mixed H 2 / H ∞ stabilization of the synchronization error dynamics. Then, both the finite and infinite horizon cases for the mixed H 2 / H ∞ synchronization control are considered. Sufficient conditions guaranteeing the existence of the solutions to the mixed H 2 / H ∞ synchronization control problem are given via a standard completing square technique. When the states of the synchronization error systems are unavailable, the Lunberger observer is designed, and the observer‐based mixed H 2 / H ∞ synchronization problem is investigated. Based on the solutions to the coupled differential Riccati equations, the optimal control for the observer‐based mixed H 2 / H ∞ synchronization control is presented. One more time, both the finite and infinite horizon cases are studied under the observer situation. Copyright © 2016 John Wiley & Sons, Ltd.