Hamilton-Jacobi-Bellman equations for Fuzzy-Dual Optimization
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- 英文论文题名：Hamilton-Jacobi-Bellman equations for Fuzzy-Dual Optimization
- 论文作者：Lunlong Zhong ; Felix Mora-Camino ; Hakim Bouadi ; Roger Marcelin Faye
- 英文论文作者：Lunlong Zhong ; Felix Mora-Camino ; Hakim Bouadi ; Roger Marcelin Faye ; Key Lab. for Adv.Signal Proc. ; Civil Aviation University of China ; Automation Research Group ; ENAC ; Toulouse University ; Ecole Militaire Polytechnique ; Electrical Eng. Dep. Université Cheik Anta Diop
- 年：2017
- 作者机构：Key Lab. for Adv.Signal Proc.,Civil Aviation University of China;Automation Research Group,ENAC,Toulouse University;Ecole Militaire Polytechnique;Electrical Eng. Dep. Université Cheik Anta Diop;
- 英文论文关键词：fuzzy-dual numbers ; uncertain systems ; Euler's equation ; optimal control ; Hamilton-Jacobi-Bellman equation
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O175
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：188k
- 原文格式：D
- 会议级别：全国
摘要
In this article, after introducing fuzzy-dual numbers, functions and functionals, the optimization of a fuzy-dual functional is considered through an extension of Euler's condition. Then, once uncertainty is imbedded in a fuzzy-dual dynamical system, the optimization of such systems is considered, leading to an extended Hamilton-Jacobi-Bellman equation to characterize optimal fuzzy-dual solutions.
In this article, after introducing fuzzy-dual numbers, functions and functionals, the optimization of a fuzy-dual functional is considered through an extension of Euler's condition. Then, once uncertainty is imbedded in a fuzzy-dual dynamical system, the optimization of such systems is considered, leading to an extended Hamilton-Jacobi-Bellman equation to characterize optimal fuzzy-dual solutions.
In this article, after introducing fuzzy-dual numbers, functions and functionals, the optimization of a fuzy-dual functional is considered through an extension of Euler's condition. Then, once uncertainty is imbedded in a fuzzy-dual dynamical system, the optimization of such systems is considered, leading to an extended Hamilton-Jacobi-Bellman equation to characterize optimal fuzzy-dual solutions.
引文
[1]Pontryagin,L.S.(1986),The Mathematical Theory of Optimal Processes,Gordon and Breach Science Publishers.
[2]Bellman,R.E.(1954).Dynamic Programming and a new formalism in the calculus of variations.Proc.Natl.Acad.Sci.40(4):231–235.
[3]R.Stengel,Optimal Control and Estimation,Dover publications,New York,1993.
[4]S.Peng,Stochastic Hamilton-Jacobi-Bellman Equation,(1992),SIAM J.Control Optim.,30(2),284–304.
[5]H.Ying,Fuzzy Control and Modelling:Analytical Foundations and Applications,Wiley-IEEE Press,2000.
[6]C.A.N.Cosenza and F.Mora-Camino,Fuzzy Dual Numbers:Theory and Applications,COPPE/UFRJ,(2016).
[7]I.S.Fisher,Dual-Number Methods in Kinematics,Statics and Dynamics,CRC Press,(1999).
[8]F.Messelmi,Analysis of Dual Functions,Annual Review of Chaos Theory,Bifurcations and Dynamical Systems,Vol.4,pp.37-54,(2013).
[9]B.Farhadinia,Pontryagin’s Minimum Principle for Fuzzy Optimal Control Problems,Iranian Journal of Fuzzy Sets,Vol.11,N°2,pp.27-43,(2014).
[10]F.Mora-Camino and R.M.Faye,Commande optimale:Approche Variationnelle,Harmattan Ed.,(2017).
[2]Bellman,R.E.(1954).Dynamic Programming and a new formalism in the calculus of variations.Proc.Natl.Acad.Sci.40(4):231–235.
[3]R.Stengel,Optimal Control and Estimation,Dover publications,New York,1993.
[4]S.Peng,Stochastic Hamilton-Jacobi-Bellman Equation,(1992),SIAM J.Control Optim.,30(2),284–304.
[5]H.Ying,Fuzzy Control and Modelling:Analytical Foundations and Applications,Wiley-IEEE Press,2000.
[6]C.A.N.Cosenza and F.Mora-Camino,Fuzzy Dual Numbers:Theory and Applications,COPPE/UFRJ,(2016).
[7]I.S.Fisher,Dual-Number Methods in Kinematics,Statics and Dynamics,CRC Press,(1999).
[8]F.Messelmi,Analysis of Dual Functions,Annual Review of Chaos Theory,Bifurcations and Dynamical Systems,Vol.4,pp.37-54,(2013).
[9]B.Farhadinia,Pontryagin’s Minimum Principle for Fuzzy Optimal Control Problems,Iranian Journal of Fuzzy Sets,Vol.11,N°2,pp.27-43,(2014).
[10]F.Mora-Camino and R.M.Faye,Commande optimale:Approche Variationnelle,Harmattan Ed.,(2017).