Inventory constraint control with uncertain stochastic demands: attractive ellipsoid technique application

In this paper, we consider the inventory robust constraint control problem with an uncertain demand. The considered system deals with a non-linear discrete-time stochastic model of a special structure. The robust control designing, consisting in the inventory product level minimization by the corresponding adjustment of the production rate, is shown to be converted into certain attractive ellipsoid ‘minimization’ problem under some specific constraints of bilinear matrix inequalities (BMI’s) type. The application of an adequate coordinate changing transforms these BMI’s into a set of linear matrix inequalities that permits to use directly the standard MATLAB-toolbox. The matrix generalization of the strong law of large numbers provides an instrument for the stochastic analyses of the considered process.