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On the synthesis of optimal nonlinear feedback laws

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Optimal Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 95))

Abstract

This paper is concerned with the automatic computation of the optimal nonlinear feedback control law, starting with a short review of the theory. The synthesis of a control system constitutes the main part of an optimization problem.

We have shown in previous papers that the optimal nonlinear feedback control law satisfies a set of partial differential equations. The knowledge of the feedback law can therefore be considered as equivalent to the computation of the hypersurface corresponding to the solution of these equations.

This hypersurface is computed off-line. Attractive features for real time implementation are discussed.

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References

  1. BOURDACHE-SIGUERDIDJANE, H. "Contribution au caloul des lois de bouclage en commande optimale non linéaire". Thèse de Docteur-Ingénieur, Université Paris XI, 1985.

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  2. BOURDACHE-SIGUERDIDJANE, H., FLIESS, M. "On the computation of optimal nonlinear feedback controls", Proc. Vth IFAC Workshop on Control Application of Nonlinear Programming and Optimization, Capri, Italy, June 11–14, 1985.

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  3. BOURDACHE-SIGUERDIDJANE, H., FLIESS, M. "Optimal feedback control of nonlinear systems", to appear in Automatica.

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  4. COURANT, R., HILBERT, D. Methods of Mathematical Physics, Vol.II. Interscience, New York, 1962.

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  5. WILLEMSTEIN, A.P., "Optimal regulation of nonlinear dynamical systems on a finite interval", SIAM J. Control Optimiz., Vol. 15, 1977, pp. 1050–1069.

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Author information

Authors and Affiliations

  1. Laboratoire des Signaux et Systèmes CNRS/ESE, Plateau du Moulon, 91190, Gif-sur-Yvette, France

    Houria Bourdache-Siguerdidjane

Authors
  1. Houria Bourdache-Siguerdidjane
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Editor information

Roland Bulirsch Angelo Miele Josef Stoer Klaus H. Well

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© 1987 Springer-Verlag

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Bourdache-Siguerdidjane, H. (1987). On the synthesis of optimal nonlinear feedback laws. In: Bulirsch, R., Miele, A., Stoer, J., Well, K.H. (eds) Optimal Control. Lecture Notes in Control and Information Sciences, vol 95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0040208

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  • DOI: https://doi.org/10.1007/BFb0040208

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17900-9

  • Online ISBN: 978-3-540-47907-9

  • eBook Packages: Springer Book Archive

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