Event-based input-constrained nonlinear H∞ state feedback with adaptive critic and neural implementation

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• 作者：Ding Wang^a ; ^b ; ^{ding.wang@ia.ac.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Chaoxu Mu^b ; ^{cxmu@tju.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Qichao Zhang^a ; ^{zhangqichao2014@ia.ac.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Derong Liu^c ; ^{derong@ustb.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Adaptive critic learning (ACL) ; Adaptive dynamic programming (ADP) ; Event-based control ; Hamilton&ndash ; Jacobi&ndash ; Isaacs (HJI) equation ; Input constraints ; Neural networks ; Nonlinear H&infin ; H&infin ; control ; State feedback
• 刊名：Neurocomputing
• 出版年：2016
• 出版时间：19 November 2016
• 年：2016
• 卷：214
• 期：Complete
• 页码：848-856
• 全文大小：1090 K

文摘

In this paper, the continuous-time input-constrained nonlinear class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0925231216307317&_mathId=si0002.gif&_user=111111111&_pii=S0925231216307317&_rdoc=1&_issn=09252312&md5=7d3c7bcbb17529a07908d000a7392bc9" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ state feedback control under event-based environment is investigated with adaptive critic designs and neural network implementation. The nonlinear class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0925231216307317&_mathId=si0003.gif&_user=111111111&_pii=S0925231216307317&_rdoc=1&_issn=09252312&md5=1f7924b164e9d12de9f641613c353ce1" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ control issue is regarded as a two-player zero-sum game that requires solving the Hamilton–Jacobi–Isaacs equation and the adaptive critic learning (ACL) method is adopted toward the event-based constrained optimal regulation. The novelty lies in that the event-based design framework is combined with the ACL technique, thereby carrying out the input-constrained nonlinear class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0925231216307317&_mathId=si0004.gif&_user=111111111&_pii=S0925231216307317&_rdoc=1&_issn=09252312&md5=8a72478e3976e87c16c9ec263caa7b37" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ state feedback via adopting a non-quadratic utility function. The event-based optimal control law and the time-based worst-case disturbance law are derived approximately, by training an artificial neural network called a critic and eventually learning the optimal weight vector. Under the action of the event-based state feedback controller, the closed-loop system is constructed with uniformly ultimately bounded stability analysis. Simulation studies are included to verify the theoretical results as well as to illustrate the event-based class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0925231216307317&_mathId=si0005.gif&_user=111111111&_pii=S0925231216307317&_rdoc=1&_issn=09252312&md5=fc990704f5bbb635322382bcfe171f8f" title="Click to view the MathML source">H_∞class="mathContainer hidden">class="mathCode">$H_{\infty }$ control performance.