Optimal Control and Positional Controllability in a One-Sector Economy

A model of production funds acquisition, which includes two differential links the zero order and series-connected inertial links, is considered in a one-sector economy. Zero-order correspond to equations Ramsey model. These contain scalar bounded control, determines distribution available into parts: investment consumption. Two describe dynamics changes volume actual at current capacity. For control system, problem posed maximize average consumption value over given time interval. The properties optimal are analytically established using Pontryagin maximum principle. cases highlighted when such bang-bang, as well when, along with bang-bang (non-singular) portions, can singular arc. At same time, concatenation non-singular portions carried out chattering. suboptimal presented, close one according quality criterion. positional terminal proposed for first approximation deviation objective function from numerically found. obtained results confirmed by corresponding numerical calculations.