The hierarchical H∞/H2-optimal control problem

In this paper a hierarchical optimal control problem is considered, which involves an H_∞ cost in the primary problem (arising from a “one-block” problem) and a quadratic secondary objective. Using results from super-optimal interpolation theory, it is shown that the problem can be reduced to a multi-disk minimisation in terms of a free parameter of reduced dimension. The problem is finally formulated as a projection onto the intersection of two closed convex sets in L₂ and it is shown that a slight modification of a technique based on the convex alternating projection algorithm, may be employed at this stage to obtain a numerical solution to the problem