Advertisement

A Theorem of the Alternative for Linear Control Systems

  • Paolo Cubiotti
Chapter
  • 425 Downloads
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 58)

Abstract

In this paper we deal with the existence of periodic extremal solutions of a linear control system. We establish an alternative theorem and we present counterexamples to possible improvements.

Keywords

Linear control systems periodic extremal solutions tangent cone relative boundary fixed points 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Hermes, JP. Lasalle, Functional Analysis and Time Optimal Control, Academic Press, New York, 1969zbMATHGoogle Scholar
  2. [2]
    E.B. Lee, L. Markus, Foundations of Optimal Control Theory, John Wiley and Sons, New York, 1967.zbMATHGoogle Scholar
  3. [3]
    P. Cubiotti, Application of quasi-variational inequalities to linear control systems, J. Optim. Theory Appl. 89 (1996), 101–113.CrossRefMathSciNetzbMATHGoogle Scholar
  4. [4]
    P. Cubiotti An existence theorem for generalized quasi-variational inequalities, Set-Valued Anal. 1 (1993), 81–87.CrossRefMathSciNetzbMATHGoogle Scholar
  5. [5]
    P. Cubiotti, N.D. Yen, A result related to Ricceri’s conjecture on generalized quasi-variational inequalities, Arch. Math. 69 (1997), 507–514.CrossRefMathSciNetzbMATHGoogle Scholar
  6. [6]
    M. De Luca, Generalized Quasi-Variational Inequalities and Traffic Equilibrium Problem. In Variational Inequalities and Network Equilibrium Problems, F. Giannessi and A. Maugeri eds., Plenum Press, New York, 1995.Google Scholar
  7. [7]
    M. De Luca M, A. Maugeri, Discontinuous Quasi-Variational Inequalities and Applications to Equilibrium Problems, In Nonsmooth Optimization. Methods and Applications, F. Giannessi ed., Gordon and Breach, 1992.Google Scholar
  8. [8]
    B. Ricceri, Basic Existence Theorems for Generalized Variational and Quasi-Variational Inequalities, In Variational Inequalities and Network Equilibrium Problems, F. Giannessi and A. Maugeri eds., Plenum Press, New York, 1995.Google Scholar
  9. [9]
    E. Michael Continuous selections I, Ann. Math. 63 (1956), 361–382.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    JP. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.zbMATHGoogle Scholar
  11. [11]
    JP. Aubin, H. Frankowska, Set-Valued Analysis, Birkhäser, Boston, 1990.zbMATHGoogle Scholar
  12. [12]
    E. Klein, A.C. Thompson, Theory of Correspondences, John Wiley and Sons, New York, 1984.zbMATHGoogle Scholar
  13. [13]
    C. Castaing, M. Moussaoui, A. Syam, Multivalued differential equations on closed convex sets in Banach spaces, Set-Valued Anal. 1 (1994), 329–3531.MathSciNetGoogle Scholar
  14. [14]
    K. Fan Fixed point and minimax theorems in locally convex topological linear spaces, Proc. Nat. Acad. Sc. USA 38 (1952), 121–126.zbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Paolo Cubiotti
    • 1
  1. 1.Department of MathematicsUniversity of MessinaMessinaItaly

Personalised recommendations