Hierarchical control by functional allotment

Abstract

AbstractMost of the studies in the past on the hierarchical control have been concerned with the computational allotment between higher and lower levels, or among lower levels. In the actual system with a hierarchical structure, however, it often happens that the functional allotment is made between higher and lower levels. From such a viewpoint, the following scheme is considered in this paper. Consider a hierarchical control scheme with a functional allotment between higher and lower levels. The higher‐level controller views the whole system by a macroscopic view, and makes decisions so that the system is optimized from a wide range of viewpoints. Then the instruction is issued toward the lower‐level controller. The lower‐level controller views his own subsystem in detail and makes finer decisions so that the subsystem is optimized, while observing the instruction from the higher level as far as possible. The problem is formulated for the hierarchical control with functional allotment, considering the controllable linear discrete‐time stochastic system with a quadratic cost function. Then a situation is assumed where the information concerning the state estimation and the control input can be exchanged at each time between the higher and lower levels, and an algorithm is derived which can successively determine the control input at each time for the higher‐ and lower‐level controllers. Furthermore, it is shown by a numerical example that the intention of the higher‐level controller is reflected on the actual control by the lower level, by a suitable definition of the cost function of the higher‐level controller.