Impulse control of observations in ellipsoidal filtering

Develops the impulse control approach to the observation process in the ellipsoidal filtering problem. The ellipsoidal filtering problem can be considered as a deterministic analog of the Kalman filtering one, where a Gaussian noise is replaced by a deterministic uncertain function enclosed in an ellipsoid, and uncertain initial conditions are enclosed in an ellipsoid as well. Except for the filtering problem considered in Bertsekas and Rhodes (1971), where uncertainties satisfy the special integral relations, the examined problem is the only known deterministic one, where uncertainties assume general geometric bounds (belong to ellipsoids) and the obtained system of filtering equations is closed with respect to two variables (the center and matrix of an ellipsoid). Impulsive modeling of the transition matrix in an observation equation generates online computable jumps of the ellipsoid matrix from its current value to zero and, as a result, enables us to obtain the estimate with zero ellipsoid matrix for all post-jump time moments