Abstract:
We consider a controlled linear differential equation. The controller
must transfer the initial state $x_0$ of the equation to a given final
state $x_T$. This process is followed by the observer, who tries to
determine $x_T$ but does not know the state vector of the equation and
obtains information via the vector $y(t)$ connected with $x(t)$. With
the aid of the signal $y(t)$, the observer can determine an
information set containing $x_T$. In the case of special constraints
for controls (or disturbances from the point of view of the observer),
the information set becomes the ellipsoid, the parameters of which are
described by the system of differential equations. In the game, the
controller, who is the main player, endeavors to accomplish its task
and maximize the information set simultaneously. An example is
considered.
Keywords:guaranteed estimation, information set, reachable set, observation control.
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