Hierarchical control for large-scale systems with general multiple linear-quadratic structure

Abstract

A class of large-scale linear control systems, where the overall objective function is a nonlinear function of multiple quadratic performance indices, is investigated in this paper. This type of large-scale control problem with a general multiple linear-quadratic structure is nonseparable in the sense of conventional hierarchical control. Hierarchical control is extended in this paper to large-scale nonseparable control problems, where multiobjective optimization is used as a separation strategy. The large-scale general multiple linear-quadratic 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 prediction 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 control of the original large-scale nonseparable control problem is attained. One feature of this hierarchical control scheme is a derived analytical solution for the large-scale general multiple linear-quadratic control.