×

Two-level hierarchical control for stochastic optimal resource allocation. (English) Zbl 0581.93004

This paper discusses a two-level hierarchical partially decentralized control for stochastic optimal resource allocation. Local conrollers of the lower level receive measurements from their own subsystems and transform them into simplified ones. The coordinator of the higher level gathers the simplified measurements from all the local controllers and takes decisions on the coordinating variables, which impose ”elastic” constraints on the local controllers. Subject to these constraints, they decide resource amounts to be supplied to their own subsystems. The problem is to determine optimal control laws of the coordinator and local controllers that minimize the losses resulting from unsatisfied demands of all the subsystems. A sufficient condition for the optimal control laws is derived under a few assumptions. A linear-quadratic problem is solved and the optimal control law of the coordinator is shown to have the certainty equivalence property.
Reviewer: K.Ohno

MSC:

93A13 Hierarchical systems
90B50 Management decision making, including multiple objectives
93E20 Optimal stochastic control
91A35 Decision theory for games
93A15 Large-scale systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] ÅSTRÖM K. J., Introduction to Stochastic Control Theory (1970)
[2] CHONG C. Y., l.E.E.E. Trans, autom. Control 16 pp 423– (1971) · doi:10.1109/TAC.1971.1099810
[3] CHU K. C., l.E.E.E. Trans, autom. Control 17 pp 22– (1972) · Zbl 0259.93060 · doi:10.1109/TAC.1972.1099854
[4] FINDEISEN W., Multilevel Control Systems (1974) · Zbl 0376.93003
[5] GESSING R., Arch. Automat. Telemech. pp 447– (1976)
[6] Ho Y. C., l.E.E.E. Trans, autom. Control 17 pp 15– (1972)
[7] Ho Y. C., Proc. Inst, elect, electron. Engrs 68 pp 644– (1980) · doi:10.1109/PROC.1980.11718
[8] Ho Y. C., l.E.E.E. Trans, autom. Control 17 pp 15– (1972) · Zbl 0259.93059 · doi:10.1109/TAC.1972.1099850
[9] KULIKOWSKI R., Control of Large–Scale Systems (1970) · Zbl 0228.49009
[10] LUENBERGER D. G., Optimization by Vector Space Method (1969) · Zbl 0176.12701
[11] SANDELL N. R., l.E.E.E. Trans, autom. Control 23 pp 108– (1978) · Zbl 0385.93001 · doi:10.1109/TAC.1978.1101704
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.