Problems of differential and topological diagnostics. Part 3. The checking problem

Proposed work is the third in the cycle, therefore, we explain such notions as checking sphere, checking ellipsoid and checking tubes. The checking problem is stated and the algorithms for solving it are formulated. The criterion for a malfunction in a controlled system whose motion is described by ordinary differential equations is taken to be the attainment of a checking surface by the checking vector. We first propose the methods for solving the checking problems in which the checking surfaces are chosen in the form of a checking sphere, checking ellipsoid or checking tube. Then we consider the general techniques for constructing the checking surface by using the statistical testing method. We also give the extended statement of the checking problem. And we also prepare the material for the consideration of the problem of diagnostics.