DESCRIPTOR APPROACH TO THE SYNTHESIS OF CONSTRAINED ROBUST GUARANTEED INVENTORY CONTROL USING PARAMETER-DEPENDENT LYAPUNOV FUNCTION

Yu. I. Dorofieiev

Abstract


The problem of robust guaranteed inventory control synthesis for supply networks with parametric uncertainty under action of unknown,
but bounded external demand and availability of non-symmetrical constraints on the values of states and controls is solved. The control law is constructed in the form of a linear dynamic feedback with respect to deviation between cash and safety stock levels of resources. In order
to suppress the influence of external perturbations, modeling changes in demand, while ensuring robust stability of the closed system the
method of invariant ellipsoids is used, which has been improved through the use descriptor system approach and building parameter-dependent
Lyapunov function, which reduces the impact degree of uncertainty of the transport time-delays on the result of the synthesis control. With
the help of the linear matrix inequalities technique the control synthesis problem is presented as a series of semidefinite programming, for
solving which is used open source software. In the framework of the proposed method is possible to choose the optimal values of safety stock levels of resources, as the resulting solution determines, in fact, an algorithmic relationship between the levels of safety stocks and the optimal value of the quality criterion. The numerical example is considered.

Keywords


inventory control, robust control, invariant ellipsoids method, descriptor approach, parameter dependent Lyapunov function, linear matrix inequality.

References


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DOI: https://doi.org/10.15588/1607-3274-2015-4-13



Copyright (c) 2016 Yu. I. Dorofieiev

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