STABLE SOLUTION OF PROBLEMS OF TRACKING AND DYNAMICAL RECONSTRUCTION UNDER MEASURING PHASE COORDINATES AT DISCRETE TIME MOMENTS

The problem of dynamic reconstruction of input actions in a system of ordinary differential equations and the problem of tracking a trajectory of a system by some trajectory of another one influenced by an unknown disturbance are under consideration. An input action is assumed to be an unbounded function, namely, an element of the space of square integrable functions. Two solving algorithms, which are stable with respect to informational noises and computational errors and oriented to program realization, are designed. Upper estimates of their convergence rates are established. The algorithms are based on constructions from feedback control theory. They operate under conditions of (inaccurate) measuring the phase states of the given systems at discrete times.