Description: An approach to solve guaranteed cost inventory control synthesis problem in discrete-time supply chains with uncertain transport delays and a quadratic cost function with “unknown but bounded” demand and the availability of non-symmetric constraints on the values of control inputs is proposed. The value of delays in each period is assumed to be unknown, but bounded by some maximum value. The problem is to design a dynamic feedback control law with respect to deviation between on hand and safety stock levels such that the closed-loop cost function value do not exceed specified upper bound for any admissible uncertainties. Sufficient conditions for the existence of such controllers are obtained on the basis of the invariant ellipsoids method using the technique of linear matrix inequalities (LMI). A parametrized characterization of the guaranteed cost controllers (if they exist) is given in terms of the feasible solution to a certain LMI set. The problem of semidefinite programming to produce the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function is formulated. Free specialized packages based on the MATLAB system are used for solving of the above problem. The important property of the obtained solution is the asymptotic stability of controlled supply chains which is guaranteed by the development of the Lyapunov direct method using Lyapunov-Krasovskii functional. A numerical example is provided.
Keywords: inventory control, guaranteed cost control, invariant ellipsoids method, Lyapunov-Krasovskii functional, linear matrix inequality, semidefinite programming