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Permanent Differential Games: Quasi Stationary and Relaxed Steady-State Operations

  • G. Guardabassi
  • N. Schiavoni

Abstract

This paper deals with permanent differential games, i.e. differential games the state of which must satisfy a periodicity constraint.

To any given permanent differential game a conventional (non- differential) game of obvious interest can be associated in a straightforward way by simply considering the equilibrium states only of the dynamical system under consideration. In this situation a comparison between the solutions of the former (dynamical) and the latter (static) game is of obvious interest. In particular, the main concern here can be expressed by the following question: Under what conditions (henceforth called dynamic dominance conditions), for a given Pareto-optimal solution of the associated static game, a nonconstant control exists such as to dominate, in the Pareto sense, the constant solution above (which is Pareto-optimal within the class of the constant solutions only)?

The approach taken in the present paper to takle such a kind of question can be considered a standard one in Periodic Optimization Theory [1] and consists in restraining the attention to special classes of control functions (namely quasi-constant and chattering controls) leading to relatively simple and general dynamic dominance conditions, each one of which calls for nothing more than the analysis of a suitable static game.

Keywords

Optimization Theory Differential Game Constant Solution Performance Vector Obvious Interest 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • G. Guardabassi
    • 1
  • N. Schiavoni
    • 1
  1. 1.Istituto di Elettrotecnica ed ElettronicaPolitecnico di MilanoMilanItaly

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