Dual Stabilization of the Multidimensional Regression Object at the Given Level

Abstract

The statement of the problem of the dual control of the regression object with multidimensional-matrix input and output variables and dynamic programming functional equations for its solution are given. The problem of the dual stabilization of the regression object at the given level is considered. The purpose of control is reaching the given value of the output variable by sequential control actions in production operation mode. In order to solve the problem, the regression function of the object is supposed to be affine in input variables, and the inner noise is supposed to be Gaussian. The sequential solution of the functional dynamic programming equations is performed. As a result, the optimal control action at the last control step is obtained. It is shown also that the obtaining of the optimal control actions at the other control steps is connected with big difficulties and impossible both analytically and numerically. The control action obtained at the last control step is proposed to be used at the arbitrary control step. This control action is called the control action with passive information accumulation. The dual control algorithm with passive information accumulation was programmed for numerical calculations and tested for a number of objects. It showed acceptable results for the practice. The advantages of the developed algorithm are theoretical and algorithmical generality.