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Proceedings Mathematical Sciences

, Volume 117, Issue 2, pp 233–257 | Cite as

Infinite dimensional differential games with hybrid controls

  • A. J. Shaiju
  • Sheetal DharmattiEmail author
Article

Abstract

A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott-Kalton, we prove the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities.

Keywords

Differential game strategy hybrid controls value viscosity solution 

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References

  1. [1]
    Bardi M and Capuzzo-Dolcetta I, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations (Birkhauser) (1997)Google Scholar
  2. [2]
    Crandall M G and Lions P L, Hamilton-Jacobi equations in infinite dimensions, Part VI: Nonlinear A and Tataru’s method refined, Evolution Equations, Control Theory and Biomathematics, Lecture Notes in Pure and Applied Mathematics, Dekker 155 (1994) 51–89MathSciNetGoogle Scholar
  3. [3]
    Evans L C and Souganidis P E, Differential games and representation formulas for Hamilton-Jacobi equations, Indiana Univ. Math. J. 33 (1984) 773–797CrossRefMathSciNetGoogle Scholar
  4. [4]
    Kocan M, Soravia P and Swiech A, On differential games for infinite-dimensional systems with nonlinear, unbounded operators, J. Math. Anal. Appl. 211 (1997) 395–423zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Pazy A, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences 44 (Springer-Verlag) (1989)Google Scholar
  6. [6]
    Yong J, Differential games with switching strategies, J. Math. Anal. Appl. 145 (1990) 455–469zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Yong J, A zero-sum differential game in a finite duration with switching strategies, SIAM J. Control Optim. 28 (1990) 1234–1250zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Yong J, Zero-sum differential games involving impulse controls, Appl. Math. Optim. 29 (1990) 243–261CrossRefMathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 2007

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.TIFR Centre, IIScCampusBangaloreIndia

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