Hierarchical control for large-scale systems

A class of large-scale systems, where the overall objective function is a nonlinear function of performance index of each subsystem, is investigated in this paper. This type of large-scale control problem is non-separable in the sense of conventional hierarchical control. Hierarchical control is extended in the paper to large-scale non-separable control problems, where multiobjective optimization is used as separation strategy. The large-scale non-separable control problem is embedded, under certain conditions, into a family of the weighted Lagrangian formulation. The weighted Lagrangian formulation is separable with respect to subsystems and can be effectively solved using the interaction balance approach at the two lower levels in the proposed three-level solution structure. At the third level, the weighting vector for the weighted Lagrangian formulation is adjusted iteratively to search the optimal weighting vector with which the optimal of the original large-scale non-separable control problem is obtained. Theoretical base of the algorithm is established. Simulation shows that the algorithm is effective.