Evasion with a single measurement of the state vector

摘要

We consider a plant whose dynamics is described by a system of linear ordinary differential equations with an unknown noise. The considered differential game has fixed terminal time. The players’ control parameters are subjected to geometric constraints in the form of closed balls. The aim of the control is to evade zero. The problem is solved with the use of control laws with a single measurement of the state vector. We present necessary conditions and a construction algorithm for the optimal measurement instant. The results are illustrated by some control systems of a special form. In particular, we consider an example in which one measurement can guarantee the result not worse than that for a refined grid of measurement points. We discuss whether this situation is typical. We also consider an example with infinitely many points at which the unique measurement can be performed.