On an algorithm for tracking the motion of the reference system with aftereffect when only part of the coordinates is measured (Q641996)

The tracking problem for a system with aftereffect is considered. The aim is to construct a feedback control law for the system such that its trajectory tracks a certain trajectory of the given reference system. The case of incomplete information on the phase trajectory is considered. Namely, it is assumed that the initial states of both systems coincide, and at some moments \(t_i\) measurements of part of the coordinates of both systems are given. Also, the measurement results for the controlled system are given with some error \(h\in(0,1)\). An algorithm for solving the described problem is presented, which is based on the method of dynamic approximation of control and employs the ``reconstruction block'' as a source of information on unknown coordinates. The algorithm provides that the phase trajectory of the controlled system remains in an \(\varepsilon\)-neighborhood of the reference trajectory during the interval of the length \(T\) if \(h<h_*(\varepsilon)\) and \(\delta=t_{i+1}-t_i<\delta_*(\varepsilon)\).