Skip to main content
Log in

Idempotent analysis as a tool of control theory and optimal synthesis. I

  • Published:
Functional Analysis and Its Applications Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. S. M. Avdoshin, V. V. Belov, and V. P. Maslov, "Application of methods of wave and geometrical optics in the architecture of modern computing systems," Usp. Mat. Nauk,39, No. 4, 108–109 (1984).

    Google Scholar 

  2. S. M. Avdoshin, V. V. Belov, and V. P. Maslov, Mathematical Aspects of Synthesis of Computing Media [in Russian], Izd. MIEM, Moscow (1984).

    Google Scholar 

  3. V. P. Maslov, "Quasilinear systems which are linear in some semimoduli," in: Congrès international sur les problemes hyperboliques, 13–17 janvier 1986, Saint-Etienne, France.

    Google Scholar 

  4. V. P. Maslov, "New superposition principle for optimisation problems," in: Séminaire équations au dérivées partielles, No. 24, Paris (1985–1986).

  5. V. P. Maslov, Asymptotic Methods for Solution of Pseudodifferential Equations [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  6. V. P. Maslov, "On a new superposition principle for optimization problems," Usp. Mat. Nauk,42, No. 3, 39–48 (1987).

    Google Scholar 

  7. V. P. Maslov, "A new approach to generalized solutions of nonlinear systems," Dokl. Akad. Nauk SSSR,292, No. 1, 37–41 (1987).

    Google Scholar 

  8. V. P. Maslov and A. M. Chebotarev, "Displacement of boundary conditions and uniqueness theorems for nonlinear boundary-value problems," Dokl. Akad. Nauk SSSR,289, No. 1, 47–51 (1987).

    Google Scholar 

  9. V. N. Kolokol'tsov and V. P. Maslov, "The Cauchy problem for the homogeneous Bellman equation," Dokl. Akad. Nauk SSSR,296, No. 4, 796–800 (1987).

    Google Scholar 

  10. V. N. Kolokol'tsov and V. P. Maslov, "General form of endomorphisms in the space of continuous functions with value in a real commutative semiring (with operation • = max)," Dokl. Akad. Nauk SSSR,295, No. 2, 283–287 (1987).

    Google Scholar 

  11. P. I. Dudnikov and S. N. Samborskii, "Endomorphisms of semimodules over semirings with an idempotent operation," Preprint, Mathematics Institute, Akad. Nauk UkrSSR, 87.48, Kiev (1987).

    Google Scholar 

  12. S. M. Avdoshin, V. V. Belov, V. P. Maslov, and A. M. Piterkin, Optimization of Flexible Production Systems [in Russian], Izd. MIEM, Moscow (1987).

    Google Scholar 

  13. V. V. Voevodin, Parallel Structures of Algorithms and Programs [in Russian], Izd. OVM Akad. Nauk SSSR (1987).

  14. S. N. Kruzhkov, Nonlinear Partial Differential Equations (Lectures), Vol. 2 [in Russian], Moscow State Univ. (1970).

  15. M. G. Crandall and P. L. Lions, "Viscosity solutions of Hamilton—Jacobi equations," Trans. Am. Math. Soc.,27, 1–40 (1983).

    Google Scholar 

  16. L. C. Evans, "Some min—max methods for the Hamilton—Jacobi equation," Indiana Univ. Math. J.,33, No. 1, 31–51 (1984).

    Google Scholar 

  17. H. Furstenberg, "Strict ergodicity and transformations of the torus," Am. J. Math.,83, No. 4, 573–601 (1961).

    Google Scholar 

  18. I. Ekeland and R. Temam, Analyse convexe et problèmes variationels, Dunod, Paris (1974).

    Google Scholar 

  19. I. V. Romanovskii, "Optimization of steady-state control of a discrete deterministic dynamic programming system," Kibernetika, No. 2, 66–78 (1967).

    Google Scholar 

  20. I. V. Romanovskii, "Asymptotic behavior of a discrete deterministic process with continuous set of states," Optimal'noe Planirovanie (Novosibirsk), No. 8, 71–93 (1967).

    Google Scholar 

  21. M. Gondran, "Path algebra and algorithms," in: Combinatorial Programming Methods and Applications, B. Roy (ed.) (1975), pp. 137–148.

Download references

Authors

Additional information

Moscow Institute of Electronic Engineering. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 23, No. 1, pp. 1–14, January–March, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kolokol'tsov, V.N., Maslov, V.P. Idempotent analysis as a tool of control theory and optimal synthesis. I. Funct Anal Its Appl 23, 1–11 (1989). https://doi.org/10.1007/BF01078568

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01078568

Keywords

Navigation