In this paper we study the optimum form of external influence with low power necessary for activation of one-dimensional dynamical system. The Lagrange multipliers method is used. Optimum influence with low power and optimum law of change of a dynamical system state are determined analytically for linear dynamical system and numerically for nonlinear dynamical system. The opportunity of influence power reduction vs its duration is investigated. The efficiency of optimum influence expressed in economy of energy quantity, spent on it, in comparison to rectangular influence is studied.
