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Infinite dimensional control problems with state constraints

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Modelling and Inverse Problems of Control for Distributed Parameter Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 154))

Abstract

We study optimal control problems for distributed parameter systems with control and state constraints by using the theory of infinite dimensional nonlinear programming problems.

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References

  1. I. EKELAND, Nonconvex minimization problems, Bull. Amer. Math. Soc. N. S. 3 (1979) 443–474

    Google Scholar 

  2. H. O. FATTORINI, A remark on the "bang — bang" principle for linear control systems in infinite dimensional spaces, SIAM J. Control 6 (1968) 109–113

    Google Scholar 

  3. H. O. FATTORINI, The time optimal control problem in Banach spaces, Appl. Math. Optimization 1 (1974) 163–188.

    Google Scholar 

  4. H. O. FATTORINI, A unified theory of necessary conditions for nonlinear nonconvex control systems, Appl. Math. Optim. 15 (1987) 141–185.

    Google Scholar 

  5. H. O. FATTORINI, Optimal control of nonlinear systems: convergence of suboptimal controls, II, Springer Lecture Notes on Control and Information Sciences 97 (1987) 230–246

    Google Scholar 

  6. H. O. FATTORINI and H. FRANKOWSKA, Necessary conditions for infinite dimensional control problems, Proceedings of 8th. International Conference on Analysis and Optimization of Systems, Antibes — Juan-Les-Pins, 1988. To appear in Lecture Notes on Control and Information Sciences.

    Google Scholar 

  7. H. O. FATTORINI AND H. FRANKOWSKA, Necessary conditions for infinite dimensional control problems, to appear in Mathematics of Control, Signals and Systems.

    Google Scholar 

  8. H. FRANKOWSKA, Estimations a priori pour les inclusions différentielles opérationnelles, C. R. Acad. Sci. Paris 308 Série I (1989) 47–50.

    Google Scholar 

  9. H. FRANKOWSKA, Some inverse mapping theorems, to appear in Annales de IHP, Analyse Nonlineaire, (1990).

    Google Scholar 

  10. I. LASIECKA, State constrained control problems for parabolic systems: regularity of optimal solutions, Appl. Math. Optimization 6 (1980) 1–29.

    Google Scholar 

  11. LI X. and YAO Y., Maximum principle of distributed parameter systems with time lags, Distributed Parameter Systems, Springer Lecture Notes in Control and Information Sciences 75 (1985) 410–127.

    Google Scholar 

  12. U. MACKENROTH, On some elliptical control problems with state constraints, Optimization 17 (1986) 595–607.

    Google Scholar 

  13. T. ROUBICEK, Generalized solutions of constrained optimization problems, SIAM J. Control and Optimization 24 (1986) 951–960.

    Google Scholar 

  14. F. TRÖLTZSCH, On some parabolic boundary control problems with constraints on the control and functional constraints on the state, Zeitschrift für Analysis und Ihre Anwend. 1 (1982) 1–13.

    Google Scholar 

  15. L. W. WHITE, Control of a hyperbolic problem with pointwise stress constraints, JOTA 41 (1983) 359–369.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 90024, Los Angeles, California, USA

    H. O. Fattorini

  2. Ceremade, Université de Paris — Dauphine, 75775, Paris CX (16), France

    H. Frankowska

Authors
  1. H. O. Fattorini
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  2. H. Frankowska
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Editor information

Alexander Kurzhanski Irena Lasiecka

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© 1991 International Federation for Information Processing

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Fattorini, H.O., Frankowska, H. (1991). Infinite dimensional control problems with state constraints. In: Kurzhanski, A., Lasiecka, I. (eds) Modelling and Inverse Problems of Control for Distributed Parameter Systems. Lecture Notes in Control and Information Sciences, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044483

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  • DOI: https://doi.org/10.1007/BFb0044483

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53583-6

  • Online ISBN: 978-3-540-46839-4

  • eBook Packages: Springer Book Archive

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