| Contents |
| Consider a motion correction problem for the linear system with integral
constraints on disturbances. It is supported that the phase vector $x(t)$ of the
system is unknown, but one can observe some linear transformation $y(t)$ of this
phase vector with an additive noise. Due to measurements, the information set
$X(t,y(\cdot))$ containing the true vector $x(t)$ can be built. The goal of the
controller (1-st player) is to minimize the terminal cost $\Phi(X(T,y(\cdot)))$.
The control strategies is formed by functions of the form $u(t,X(t,y(\cdot)))$
depending on the position $(t,X(t,y(\cdot)))$. The initial minimax problem of
motion correction can be reduced to the differential game with complete
information, in which the second player may choose the disturbances. We prove the
existence of the saddle point of the game and suggest a constructive method of
building of optimal strategies. The results of N.N. Krasovski, A.B. Kurzhanski, and
A.I. Subbotin are used. Some results of computer simulations are given. An
application to the problem of coordinate alignment of navigation devices for a
transport ship-airplane system is also considered. |
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