Mixed H₂/H_∞ fuzzy proportional-spatial integral control design for a class of nonlinear distributed parameter systems

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• 作者：Jun-Wei Wang^a ; ^{junweiwang@ustb.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Huai-Ning Wu^b ; Yao Yu^a ; Chang-Yin Sun^a
• 关键词：Distributed parameter systems ; Exponential stability ; Proportional-spatial integral control ; Takagi&ndash ; Sugeno (T&ndash ; S) fuzzy model ; Linear matrix inequalities (LMIs)
• 刊名：Fuzzy Sets and Systems
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：306
• 期：Complete
• 页码：26-47
• 全文大小：1073 K

文摘

In this paper, a fuzzy feedback control design problem with a mixed user=111111111&_pii=S0165011416000257&_rdoc=1&_issn=01650114&md5=26db6d5af2a63c2c772d211fb536db7d" title="Click to view the MathML source">H₂/H_∞$H_2/H_{\infty }$ 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 user=111111111&_pii=S0165011416000257&_rdoc=1&_issn=01650114&md5=26db6d5af2a63c2c772d211fb536db7d" title="Click to view the MathML source">H₂/H_∞$H_2/H_{\infty }$ 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 user=111111111&_pii=S0165011416000257&_rdoc=1&_issn=01650114&md5=26db6d5af2a63c2c772d211fb536db7d" title="Click to view the MathML source">H₂/H_∞$H_2/H_{\infty }$ 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 user=111111111&_pii=S0165011416000257&_rdoc=1&_issn=01650114&md5=c0cfb0e2fd729fbe9f69029f02058577" title="Click to view the MathML source">H_∞$H_{\infty }$ fuzzy controller is derived in the sense of minimizing an upper bound of a given user=111111111&_pii=S0165011416000257&_rdoc=1&_issn=01650114&md5=5dbcf80e865de20cb307d0c7aaedfd94" title="Click to view the MathML source">H₂$H_2$ performance function. Finally, the developed design methodology is successfully applied to feedback control of a semi-linear reaction–diffusion system with spatial integral terms.