Hierarchical H∞/H2 optimal control:: 2-block problem

A two level hierarchical H-infinity/H-2 optimal control problem is considered. A novel affine parametrization of the optimal solution set corresponding to the primary objective is used to transform the problem to a multidisk optimization in terms of a matrix parameter of reduced dimensions. A detailed cancellation analysis is performed to obtain a low order state space realization of a generalized plant which is used to solve the second-level problem. A convex alternating projections method is used to solve a resulting feasibility problem which gives a high-order FIR filter in terms of its Markov parameters. This is finally approximated by a low-order IIR filter.