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An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm.

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Title: An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm.
Authors: Milic, Vladimir1, Kasac, Josip1, Novakovic, Branko1
Source: International Journal of Systems Science. Oct2015, Vol. 46 Issue 13, p2448-2460. 13p.
Subjects: Fuzzy logic, Nonlinear systems, Mathematical optimization, Weierstrass-Stone theorem, Approximation theory
Abstract: This paper is concerned with-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone–Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton’s method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system. [ABSTRACT FROM PUBLISHER]
Copyright of International Journal of Systems Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 108329695
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  Data: An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm.
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  Data: <searchLink fieldCode="AR" term="%22Milic%2C+Vladimir%22">Milic, Vladimir</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Kasac%2C+Josip%22">Kasac, Josip</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Novakovic%2C+Branko%22">Novakovic, Branko</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Systems+Science%22">International Journal of Systems Science</searchLink>. Oct2015, Vol. 46 Issue 13, p2448-2460. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Fuzzy+logic%22">Fuzzy logic</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Weierstrass-Stone+theorem%22">Weierstrass-Stone theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink>
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  Data: This paper is concerned with-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone–Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton’s method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system. [ABSTRACT FROM PUBLISHER]
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  Data: <i>Copyright of International Journal of Systems Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/00207721.2013.860640
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        Text: English
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        PageCount: 13
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      – SubjectFull: Fuzzy logic
        Type: general
      – SubjectFull: Nonlinear systems
        Type: general
      – SubjectFull: Mathematical optimization
        Type: general
      – SubjectFull: Weierstrass-Stone theorem
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      – SubjectFull: Approximation theory
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      – TitleFull: An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm.
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            NameFull: Milic, Vladimir
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              Text: Oct2015
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              Y: 2015
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