Asymptotics of Optimal Synthesis for One Class of Extremal Problems

The asymptotics of an optimal control while approaching the origin is found for a class of mean square deviation minimization problems with a unilateral force. The asymptotics is described by a series of impulses of maximal amplitude that decrease in time and have the support in the neighborhoods of points of a certain infinite arithmetic progression. The results are applied to the investigation of controlled populational dynamics described by the Lottka–Volterra–Kolmogorov equations.