On the problem of impulse measurement feedback control

A problem of impulse measurement feedback control is considered with noisy observations. The solution scheme is based on dynamic programming techniques in the form of analogs of Hamiltonian formalism equations, and the solution is a sequence of delta functions. The sets of state vectors compatible with a priori data and current measurements are considered as the information state of the system. Observation models are considered either as continuous with "uncertain" disturbances, for which there is no statistical description, or as stochastic and discrete ones coming from a communication channel in the form of a Poisson flow with disturbances that are distributed uniformly over a given set. All the results are obtained by means of operations in a finite-dimensional space. Computation schemes are discussed. Examples of numerical modeling are presented.