Decentralized Guaranteed Cost Inventory Control of Supply Networks with Uncertain Delays
Leonid M. Lyubchyk, Yuri Dorofieiev · River Publishers eBooks · 2022
The problem of guaranteed cost inventory control of supply networks with uncertain transport delays in the presence of disturbances modeling the changing demand is considered. As a model of uncertainty of demand, a model of “unknown but bounded” disturbance was adopted. The supply network model is adopted in the form of a graph with nodes described by discrete models in the state space, in which resource stock levels are used. An equivalent model of the system, taking into account the presence of a transport delay, is obtained using the descriptor transformation and delay-dependent Lyapunov-Krasovskii functional used for stability analysis is constructed. The solution of the problem of decentralized guaranteed cost inventory control under conditions of uncertain demand is obtained on the basis of the method of invariant ellipsoids. Using the technique of linear matrix inequalities, the problem of controller’s synthesis, which minimizes the upper boundary value of the quadratic quality criterion, is reduced to the problem of semidefinite programming. Equations of local stabilizing controllers for nodes of supply network are obtained taking into account the uncertain delay. Stability analysis of large-scale controlled supply network, taking into account the interconnections between the nodes, is obtained on the basis of Lyapunov vector functions method using the dynamic aggregated comparison system. The results of computer simulation of supply network with decentralized guaranteed cost control are also presented.