Vol.3, No 15, 2003 pp.1127-1132
UDC 681.5.01
Invited Paper

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VECTOR OPTIMIZATION AND DIFFERENTIAL GAMES
Dragovan M. Perišić
Faculty of transport and traffic engineering, University of Belgrade
Vojvode Stepe 305, Belgrade, Yugoslavia
E-mail: dragovan@sf.sf.bg.ac.yu

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Abstract. The problem of optimal control with a vector criterion, reduced to non-cooperative differential game is defined. For a given problem the necessary and sufficient conditions are given, satisfying equilibrium strategies for measurable equilibrium controls and the conditions for the existence of equilibrium minimizing controls. In the problem under consideration there are constraints to the phase coordinate, controls and unknown parameters; to every participant in the game a part of these values belongs and particular control components can take unlimited values.
Key words:  vector criterion, differential games, equilibrium controls,
minimizing process.

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VEKTORSKA OPTIMIZACIJA I DIFERENCIJALNE IGRE Definiše se problem optimalnog upravljanja sa vektorskim kriterijumom, koji se svodi na bezkoalicionu diferencijalnu igru. Za dati problem definišu se potrebni i dovoljni uslovi, koje zadovoljavaju ravnotežne strategije za merljiva ravnotežna upravljanja i uslovi postojanja ravnotežnih minimizirajućih upravljanja. U posmatranom problemu postoje ograničenja na fazne koordinate, upravljanja i nepoznate parametre, od kojih svakom učesniku u igri pripada jedan deo tih veličina, a pojedine komponente upravljanja mogu uzimati i neograničene vrednosti.