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Time-optimal control policies for cascaded production-inventory systems with control and state constraints. (English) Zbl 0531.90042
Summary: In this paper time-optimal control policies are derived for models of production-inventory systems consisting of a cascade of basic production- inventory systems with control and state constraints. The analytic solution is due to a decoupling of the complete system into its subsystems by a recursive definition of the cascaded system. It is shown that there is at least one bang-bang controlled subsystem. For the ’other’ subsystems singular control policies are obtained. Introducing a pseudo-bang-bang control for these systems it is demonstrated that by strengthening the constraints there is a continuous transition from a singular to a bang-bang control.

MSC:
90B30 Production models
93A99 General systems theory
49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
90B05 Inventory, storage, reservoirs
93C15 Control/observation systems governed by ordinary differential equations
93C99 Model systems in control theory
93C10 Nonlinear systems in control theory
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[1] DOI: 10.1080/00207728008967066 · Zbl 0451.49024 · doi:10.1080/00207728008967066
[2] GTKSANOV I. V., Lectures on Mathematical Theory of Extremum Problems (1972)
[3] DOI: 10.1109/TAC.1972.1099982 · Zbl 0259.49004 · doi:10.1109/TAC.1972.1099982
[4] DOI: 10.1016/0022-247X(71)90219-8 · Zbl 0188.47203 · doi:10.1016/0022-247X(71)90219-8
[5] DOI: 10.1137/0315023 · Zbl 0358.49008 · doi:10.1137/0315023
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