Pure strategies for quasi-positional functionals

Part of the Systems & Control: Foundations & Applications book series (SCFA)


In this chapter we consider the same problem as in Chapters I and II but for functionals γ(i) combining typical estimates of the motion of x-system and also the actions u and v. We call these functionals γ(i) quasi-positional because the optimal strategies u0(i)(·) = u0(i)(y(i),ε) and u0(i)(·) = (y(i), ε) are based on the information images y(i) that can include now not only current position {t, x} of the controlled x-system but also other variables. We give some Classification of these functionals γ(i) and describe an effective computation of the values of the game ρ(i)(y(i)) and constructions of the pure optimal strategies u0(i)(·) and u0(i)(·) which form the saddle point in the corresponding differential games.


Saddle Point Control Action Optimal Strategy Quality Index Time Moment 
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Copyright information

© Birkhäuser Boston 1995

Authors and Affiliations

  1. 1.Faculty of Mathematics and MechanicsUral State UniversityEkaterinburgRussia
  2. 2.Institute of Mathematics and MechanicsEkaterinburg GSPRussia

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