On a Linear Control Problem under Interference with a Payoff Depending on the Modulus of a Linear Function and an Integral

Abstract

We consider the problem of controlling the rod, which is attached to the rotor of the electric motor. The control is the value of the voltage applied to the electric motor. The quality criterion is the sum of the angle deviation module that forms the rod with the vertical axis, at a given time, and the integral of the square of the voltage value. We take nonlinear addend in the Lagrange equation of the system as interference. After that, this problem becomes an example of a more general linear control problem under the action of an uncontrolled interference. Applying the results obtained for such problems in the previous works of one of the authors, we construct optimal voltage in the problem of controlling the rod.