Guarantee optimization in control problems. (Optimizatsiya garantii v zadachakh upravleniya). (Russian) Zbl 0542.90106

Subbotin, A. I.; Chentsov, A. G.

Moskva: “Nauka”. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury. 288 p. R. 2.20 (1981).

Control problems under conditions of uncertainty are considered. Trajectories of controlled systems are assumed to be describable with the aid of ordinary differential equations. The problem is formulated in terms of differential games. The existence of equilibrium points is considered. Necessary and sufficient conditions for a piecewise smoothed potential of a differential game are derived. These conditions are in force even for singular surfaces. Moreover, the method for solving a differential game with the aid of a sequence of programming problems is developed. This approach leads to a new classification of differential games.

Reviewer: W.Stanczak

MSC:

91A23	Differential games (aspects of game theory)
91A99	Game theory
49J15	Existence theories for optimal control problems involving ordinary differential equations
34H05	Control problems involving ordinary differential equations
93C15	Control/observation systems governed by ordinary differential equations
91-02	Research exposition (monographs, survey articles) pertaining to game theory, economics, and finance

Keywords:

control problems; conditions of uncertainty; existence of equilibrium points; piecewise smoothed potential