Advertisement

Linear Discrete Pareto-Nash-Stackelberg Control Processes with Echoes and Retroactive Future

  • Valeriu UngureanuEmail author
Chapter
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 89)

Abstract

Mathematical models of linear discrete Pareto-Nash-Stackelberg processes with echoes and retroactive future develop the mathematical models of Pareto-Nash-Stackelberg control exposed in the precedent chapters and introduced initially in (Ungureanu, Computer Science Journal of Moldova, 21, No. 1:(61), 65–85,2013) [1]. Applications of a straightforward method along with Pontryagin’s principle produce important theoretical and practical results for the investigated models. Software benchmarking confirms and illustrates the value of the obtained results.

References

  1. 1.
    Ungureanu V. 2013. Linear discrete-time Pareto-Nash-Stackelberg control problem and principles for its solving. Computer Science Journal of Moldova, 21, No. 1:(61), 65–85.Google Scholar
  2. 2.
    Ungureanu, V. 2008. Solution principles for simultaneous and sequential games mixture. ROMAI Journal 4 (1): 225–242.MathSciNetzbMATHGoogle Scholar
  3. 3.
    Ungureanu, V., and V. Lozan. 2013. Linear discrete-time set-valued Pareto-Nash-Stackelberg control processes and their principles. ROMAI Journal 9 (1): 185–198.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F. 1961. Mathematical theory of optimal processes. Moscow: Nauka, 1961, 393 pp. (in Russian).Google Scholar
  5. 5.
    Bellman, R. 1957. Dynamic Programming, 365. New Jersey: Princeton University Press.zbMATHGoogle Scholar
  6. 6.
    Von Stackelberg, H. 1934. Marktform und Gleichgewicht (Market Structure and Equilibrium). Vienna: Springer Verlag, XIV+134 pp. (in German).Google Scholar
  7. 7.
    Nash, J. 1951. Noncooperative games. Annals of Mathematics 54 (2): 280–295.CrossRefGoogle Scholar
  8. 8.
    Von Neumann, J., and Morgenstern, O. 1944. Theory of Games and Economic Behavior. Princeton, New Jersey: Annals Princeton University Press, (2nd edn., 1947), 674 pp.Google Scholar
  9. 9.
    Leitmann, G. 1978. On Generalized Stackelberg Strategies. Journal of Optimization Theory and Applications 26: 637–648.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Nahorski, Z., H.F. Ravn, and R.V.V. Vidal. 1983. Optimization of Discrete Time System: the Upper Boundary Approach, vol. 51, 139., Lecture Notes in Control and Information Sciences Berlin: Springer.Google Scholar
  11. 11.
    Ter-Krikorov, A.M. 1977. Optimal Control ans Mathematical Economy. Moscow: Nauka, 217 pp. (in Russian).Google Scholar
  12. 12.
    Anderson, B.D.O., and J.B. Moore. 1971. Linear Optimal Control, 413. New Jersey: Prentice-Hall Inc, Englewood Cliffs.Google Scholar
  13. 13.
    Ashmanov, S.A., and A.V. Timohov. 1991. The optimization theory in problems and exercises, 142–143. Moscow: Nauka.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceMoldova State UniversityChișinăuMoldova

Personalised recommendations