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

Author

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  • Vladimir Milic
  • Josip Kasac
  • Branko Novakovic

Abstract

This paper is concerned with L2$\mathcal {L}_2$-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 L2$\mathcal {L}_2$-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.

Suggested Citation

  • Vladimir Milic & Josip Kasac & Branko Novakovic, 2015. "An analytical fuzzy-based approach to -gain optimal control of input-affine nonlinear systems using Newton-type algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(13), pages 2448-2460, October.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:13:p:2448-2460
    DOI: 10.1080/00207721.2013.860640
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