Optimal control laws for two-level hierarchical resource allocation

The optimal control laws for resource allocation realized in a two-level, hierarchical, partially decentralized control structure are considered. It is assumed that the coordinator, as well as the local controllers have different information. The linear, dynamic system composed of M subsystems, related by a common allocated resource is considered. The performance index has the shape of an expected quadratic form. The so-called elastic constraint of the control variable is used for coordination. This constraint admits some freedom in taking decisions by the local controllers, owing to that, their more detailed information can be better utilized. The optimal control laws of all decision-makers are linear and are defined by the Two-Level Certainty Equivalence Principle.