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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
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