Description: An approach to the solution of the optimal inventory control under “unknown but bounded” external demand and the availability of structural constraints using the discrete non-stationary linear PID controller in the feedback loop is proposed. The approach is based on the use of quadratic Lyapunov functions, through which the description of the invariant attainability ellipsoids of a close-loop system under the action of bounded perturbations is implemented. Using the Linear Matrix Inequalities allowed to formulate the synthesis problem as a sequence of semidefinite programming, for solution which is used specialized packages based on the MATLAB system. A numerical example is considered.
Keywords: inventory control, model predictive control, invariant ellipsoids method, linear matrix inequality, semidefinite programming