Journal
SCIENCE CHINA-MATHEMATICS
Volume 59, Issue 1, Pages 1-18Publisher
SCIENCE PRESS
DOI: 10.1007/s11425-015-5107-0
Keywords
synchronization; exact boundary synchronization; approximate boundary synchronization; coupled system of wave equations; Dirichlet boundary controls
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Funding
- National Basic Research Program of China [2013CB834100]
- National Natural Science Foundation of China [111211101]
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In this survey paper, the synchronization will be initially studied for infinite dimensional dynamical systems of partial differential equations instead of finite dimensional systems of ordinary differential equations, and will be connected with the control theory via boundary controls in a finite time interval. More precisely, various kinds of exact boundary synchronization and approximate boundary synchronization will be introduced and realized by means of fewer boundary controls for a coupled system of wave equations with Dirichlet boundary controls. Moreover, as necessary conditions for various kinds of approximate boundary synchronization, criteria of Kalman's type are obtained. Finally, some prospects will be given.
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