TY - JOUR
T1 - Sampled-data fuzzy control for a class of nonlinear parabolic distributed parameter systems under spatially point measurements
AU - Wang, Zi-Peng
AU - Li, Han-Xiong
AU - Wu, Huai-Ning
PY - 2019/11/1
Y1 - 2019/11/1
N2 - In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.
AB - In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method.
KW - Distributed parameter systems
KW - Exponential stability
KW - Fuzzy control
KW - Linear matrix inequality (LMI)
KW - Sampled-data control
UR - http://www.scopus.com/inward/record.url?scp=85060642504&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85060642504&origin=recordpage
U2 - 10.1016/j.fss.2019.01.011
DO - 10.1016/j.fss.2019.01.011
M3 - 21_Publication in refereed journal
VL - 374
SP - 60
EP - 81
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
SN - 0165-0114
ER -