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 a nalytically 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 .