Premium
Boundary output feedback stabilization for a class of coupled parabolic systems
Author(s) -
He Chao,
Li Junmin
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4472
Subject(s) - backstepping , control theory (sociology) , mathematics , nonlinear system , observer (physics) , boundary (topology) , norm (philosophy) , state observer , controller (irrigation) , control (management) , mathematical analysis , adaptive control , computer science , agronomy , physics , quantum mechanics , artificial intelligence , political science , law , biology
In this paper, the boundary output feedback stabilization problem is addressed for a class of coupled nonlinear parabolic systems. An output feedback controller is presented by introducing a Luenberger‐type observer based on the measured outputs. To determine observer gains, a backstepping transform is introduced by choosing a suitable target system with nonlinearity. Furthermore, based on the state observer, a backstepping boundary control scheme is presented. With rigorous analysis, it is proved that the states of nonlinear closed‐loop system including state estimation and estimation error of plant system are locally exponentially stable in the L 2 norm. Finally, a numerical example is proposed to illustrate the effectiveness of the presented scheme.