Descriptor system approach to the synthesis of decentralized guaranteed cost inventory control in supply networks with uncertain delays
Abstract
The approach for solving the decentralized guaranteed cost inventory control synthesis problem in supply chains with uncertain transport delays under the conditions of the "unknown but bounded" demand is proposed. The value of delays in each period is assumed to be unknown, but bounded by some maximum value. Using the descriptor transformation of the discrete model of the supply network node, the Lyapunov-Krasovskii functional that depends on the maximum value of the delay is constructed. It is proved that none increasing of this functional along any trajectory of the closed local subsystem guarantees asymptotic stability of such subsystem. The condition of existence for controller that implements a local control law in the form of linear feedback with respect to deviation between on hand and safety stock levels is obtained. The problem of the controller synthesis, which minimizes the upper boundary value of the quadratic quality criterion, is reduced to the problem of semidefinite programming on the basis of the invariant ellipsoids method using the technique of linear matrix inequalities. The vector Lyapunov functions method and the comparison method are used to analyze the stability of a decentralized inventory control system in supply chain. A numerical example is provided.
Keywords
