L 2 model reduction - Nongradient approach

The exact models of many systems are often too complex for simulation and control design. It is therefore desirable to simplify the mathematical description of the modelled systems. In this paper we consider the classical approach to model reduction, based on the minimization of the L 2 norm of the output error, i.e. of the difference between impulse responses of the original and the reduced-order model. Such index is a particularly meaningful from the technical point of view but is computationally demanding from algorithmic point of view. Corresponding optimization problem is an ill-conditioned one. Objective functional to be minimized is characterized by existence of many local minima. Additionally, it is often "flat" in a neighbourhood of a local minimum. This means, that gradient algorithms fail to give a satisfactory solution. In the paper, after analyzing properties of the mathematical programming problem to be solved, a family of non-gradient algorithms is presented.