On general multiple linear-quadratic control problems

General multiple linear-quadratic control problems are studied, where the overall objective is a nonlinear function of multiple quadratic performance indices. A multilevel solution procedure is proposed to obtain an analytical linear control law for this nonseparable control problem. The auxiliary Lagrangian problem formulated at the lower level is of a parametric linear-quadratic structure, in which the weighting vector is adjusted by the upper level until a derived optimal condition is met.<
>