On synthesis in a differential game
The control problem is considered with minimization of the guaranteed result for a system described by an ordinary differential equation in the presence of uncontrolled noise. It is shown that, when forming the optimal control by the method of programmed stochastic synthesis, the exremal shift at the accompanying point can be reduced to extremal shift against the gradient of the appropriate function. This explains the connection between the programmed stochastic synthesis and the generalized Hamilton-Jacobi equation in the theory of differential games.
scientific article; zbMATH DE number 4023071