TY - JOUR
T1 - Mixed H2/H∞ fuzzy proportional-spatial integral control design for a class of nonlinear distributed parameter systems
AU - Wang, Jun Wei
AU - Wu, Huai Ning
AU - Yu, Yao
AU - Sun, Chang Yin
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - In this paper, a fuzzy feedback control design problem with a mixed H2/H∞ performance is addressed by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distributed parameter systems represented by semi-linear parabolic partial differential-integral equations (PDIEs). The objective of this paper is to develop a fuzzy distributed P-sI controller with a mixed H2/H∞ performance index for the semi-linear parabolic PDIE system. To do this, the semi-linear parabolic PDIE system is first assumed to be exactly represented by a Takagi–Sugeno (T–S) fuzzy parabolic PDIE model in a given local domain of Hilbert space. Then, based on the T–S fuzzy PDIE model, a distributed fuzzy P-sI state feedback controller is proposed such that the closed-loop PDIE system is locally exponentially stable with a mixed H2/H∞ performance. The sufficient condition on the existence of the fuzzy controller is given by using the Lyapunov's direct method, the technique of integration by parts, and vector-valued Wirtinger's inequalities, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal H∞ fuzzy controller is derived in the sense of minimizing an upper bound of a given H2 performance function. Finally, the developed design methodology is successfully applied to feedback control of a semi-linear reaction–diffusion system with spatial integral terms.
AB - In this paper, a fuzzy feedback control design problem with a mixed H2/H∞ performance is addressed by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distributed parameter systems represented by semi-linear parabolic partial differential-integral equations (PDIEs). The objective of this paper is to develop a fuzzy distributed P-sI controller with a mixed H2/H∞ performance index for the semi-linear parabolic PDIE system. To do this, the semi-linear parabolic PDIE system is first assumed to be exactly represented by a Takagi–Sugeno (T–S) fuzzy parabolic PDIE model in a given local domain of Hilbert space. Then, based on the T–S fuzzy PDIE model, a distributed fuzzy P-sI state feedback controller is proposed such that the closed-loop PDIE system is locally exponentially stable with a mixed H2/H∞ performance. The sufficient condition on the existence of the fuzzy controller is given by using the Lyapunov's direct method, the technique of integration by parts, and vector-valued Wirtinger's inequalities, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, by using the existing LMI optimization techniques, a suboptimal H∞ fuzzy controller is derived in the sense of minimizing an upper bound of a given H2 performance function. Finally, the developed design methodology is successfully applied to feedback control of a semi-linear reaction–diffusion system with spatial integral terms.
KW - Distributed parameter systems
KW - Exponential stability
KW - Linear matrix inequalities (LMIs)
KW - Proportional-spatial integral control
KW - Takagi–Sugeno (T–S) fuzzy model
UR - https://www.scopus.com/pages/publications/84956639925
U2 - 10.1016/j.fss.2016.01.004
DO - 10.1016/j.fss.2016.01.004
M3 - 文章
AN - SCOPUS:84956639925
SN - 0165-0114
VL - 306
SP - 26
EP - 47
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -