Solving multiobjective random interval programming problems by a capable neural network framework

In this paper, the stability of a class of nonlinear control systems is analyzed. We first construct an optimal control problem by inserting a suitable performance index, which this problem is referred to as an infinite horizon problem. By a suitable change of variable, the infinite horizon problem...

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Published in:	Applied intelligence (Dordrecht, Netherlands) Vol. 49; no. 4; pp. 1566 - 1579
Main Authors:	Arjmandzadeh, Ziba, Nazemi, Alireza, Safi, Mohammadreza
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2019 Springer Nature B.V
Subjects:	Artificial Intelligence Computer Science Control stability Control systems design Controllers Dynamic stability Feedback control Machine learning Machines Manufacturing Mechanical Engineering Multiple objective analysis Neural networks Nonlinear analysis Nonlinear control Nonlinear programming Nonlinear systems Optimal control Performance indices Processes Stability analysis Random interval parameters Neural network models Satisficing solution Stability Fractile model Convergence
ISSN:	0924-669X, 1573-7497
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Abstract	In this paper, the stability of a class of nonlinear control systems is analyzed. We first construct an optimal control problem by inserting a suitable performance index, which this problem is referred to as an infinite horizon problem. By a suitable change of variable, the infinite horizon problem is reduced to a finite horizon problem. We then present a feedback controller designing approach for the obtained finite horizon control problem. This approach involves a neural network scheme for solving the nonlinear Hamilton Jacobi Bellman (HJB) equation. By using the neural network method, an analytic approximate solution for value function and suboptimal feedback control law is achieved. A learning algorithm based on a dynamic optimization scheme with stability and convergence properties is also provided. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed plan. As a real life application in engineering, the stabilization of a micro electro mechanical system is studied.
AbstractList	In this paper, the stability of a class of nonlinear control systems is analyzed. We first construct an optimal control problem by inserting a suitable performance index, which this problem is referred to as an infinite horizon problem. By a suitable change of variable, the infinite horizon problem is reduced to a finite horizon problem. We then present a feedback controller designing approach for the obtained finite horizon control problem. This approach involves a neural network scheme for solving the nonlinear Hamilton Jacobi Bellman (HJB) equation. By using the neural network method, an analytic approximate solution for value function and suboptimal feedback control law is achieved. A learning algorithm based on a dynamic optimization scheme with stability and convergence properties is also provided. Some illustrative examples are employed to demonstrate the accuracy and efficiency of the proposed plan. As a real life application in engineering, the stabilization of a micro electro mechanical system is studied.
Author	Arjmandzadeh, Ziba Nazemi, Alireza Safi, Mohammadreza
Author_xml	– sequence: 1 givenname: Ziba surname: Arjmandzadeh fullname: Arjmandzadeh, Ziba organization: Department of Mathematics, Semnan University – sequence: 2 givenname: Alireza surname: Nazemi fullname: Nazemi, Alireza email: nazemi20042003@gmail.com organization: Faculty of Mathematical Sciences, Shahrood University of Technology – sequence: 3 givenname: Mohammadreza surname: Safi fullname: Safi, Mohammadreza organization: Department of Mathematics, Semnan University
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Cites_doi	10.1016/j.neucom.2004.11.009 10.1007/978-1-4757-2495-0 10.1214/aoms/1177698328 10.1016/j.amc.2007.12.029 10.1016/j.ins.2006.11.007 10.1007/s10107-002-0350-x 10.1016/j.neucom.2006.10.038 10.1016/j.neunet.2016.12.007 10.1287/mnsc.13.9.672 10.1007/s10898-012-9897-0 10.1023/A:1009917818868 10.1515/9783110853698 10.1016/0165-0114(87)90028-5 10.1142/S012906570600069X 10.1093/oso/9780198534778.001.0001 10.1109/TCS.1986.1085953 10.1109/72.548188 10.1016/j.apm.2014.09.018 10.1080/23302674.2016.1224951 10.1016/j.chaos.2006.05.037 10.1007/s10589-013-9605-0 10.1007/s11155-005-3616-1 10.1016/j.neunet.2004.05.006 10.1109/TNN.2004.824252 10.1145/564585.564604 10.1016/j.fss.2005.03.001 10.1007/s12597-012-0078-1 10.1016/j.cnsns.2011.08.035 10.1007/978-1-4419-8402-9 10.1016/j.neucom.2008.05.013 10.1016/j.cam.2011.08.012 10.3906/mat-1509-65
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Keywords	Random interval parameters Neural network models Satisficing solution Stability Fractile model Convergence
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Snippet	In this paper, the stability of a class of nonlinear control systems is analyzed. We first construct an optimal control problem by inserting a suitable...
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SubjectTerms	Artificial Intelligence Computer Science Control stability Control systems design Controllers Dynamic stability Feedback control Machine learning Machines Manufacturing Mechanical Engineering Multiple objective analysis Neural networks Nonlinear analysis Nonlinear control Nonlinear programming Nonlinear systems Optimal control Performance indices Processes Stability analysis
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Title	Solving multiobjective random interval programming problems by a capable neural network framework
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