Least inventory control of multi-storage systems with non-stochastic unknown inputs

We consider multi-inventory production systems with control and state constraints dealing with unknown demand or supply levels. Unlike most articles in the literature concerning this class of systems, we cope with uncertainties in an "unknown-but-bounded" fashion, in the sense that each unknown quantity may take any value in an assigned interval. For these situations, we perform a worst-case analysis. We show that a "smallest worst-case inventory level" exists, and it is associated to a steady state control strategy. We then consider the problem of driving the inventory levels to their smallest worst-case values. For this problem, we first give necessary and sufficient conditions, then we show that convergence occurs in a finite number of steps, and we give an upper bound for such a number. This is a conference version of the paper in which the proofs, details and references are included.

[1]  Giorgio Gallo,et al.  Directed Hypergraphs and Applications , 1993, Discret. Appl. Math..

[2]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[3]  Jay E. Aronson,et al.  A survey of dynamic network flows , 1989 .

[4]  Franco Blanchini,et al.  A Network Design Problem for a Distribution System with Uncertain Demands , 1997, SIAM J. Optim..

[5]  A. Segall,et al.  An optimal control approach to dynamic routing in networks , 1982 .

[6]  M. Papageorgiou,et al.  A linear programming approach to large-scale linear optimal control problems , 1995, IEEE Trans. Autom. Control..

[7]  Fred W. Glover,et al.  Network models in optimization and their applications in practice , 1992 .

[8]  Anthony Ephremides,et al.  Control and optimization methods in communication network problems , 1989 .

[9]  Franco Blanchini,et al.  A feedback strategy for periodic network flows , 1996 .

[10]  F. Schweppe,et al.  Control of linear dynamic systems with set constrained disturbances , 1971 .

[11]  J.-C. Hennet,et al.  Etats atteignables et états d'équilibre de systèmes de production linéaires en temps discret sous contraintes , 1990 .

[12]  A. Barrett.  Network Flows and Monotropic Optimization. , 1984 .

[13]  D. Bertsekas.  Infinite time reachability of state-space regions by using feedback control , 1972 .

[14]  W. Ukovich,et al.  Linear programming approach to the control of discrete-time periodic systems with uncertain inputs , 1993 .

[15]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[16]  M. Sznaier,et al.  Persistent disturbance rejection via static-state feedback , 1995, IEEE Trans. Autom. Control..

[17]  James B. Orlin,et al.  Minimum Convex Cost Dynamic Network Flows , 1984, Math. Oper. Res..

[18]  J. Shamma.  Nonlinear state feedback for l 1 optimal control , 1993 .

[19]  Qing Zhang,et al.  Minimax production planning in failure-prone manufacturing systems , 1995 .

[20]  Franco Blanchini,et al.  A dynamic game model for distribution problems with non-stochastic uncertainty , 1996 .

[21]  Edward J. Davison,et al.  Decentralized Robust Control for Dynamic Routing of Large Scale Networks , 1990, 1990 American Control Conference.

[22]  Thomas L. Magnanti,et al.  Network Design and Transportation Planning: Models and Algorithms , 1984, Transp. Sci..

[23]  Warren B. Powell,et al.  Stochastic and dynamic networks and routing , 1995 .

[24]  Stanley B. Gershwin,et al.  An algorithm for the computer control of a flexible manufacturing system , 1983 .