Permanent Differential Games: Quasi Stationary and Relaxed Steady-State Operations
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  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.
KeywordsOptimization Theory Differential Game Constant Solution Performance Vector Obvious Interest
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