Easy ways to design inputs to obtain uncorrelated outputs in MIMO system identification

The traditional way of exciting a system with multiple inputs and multiple outputs (MIMO) for identification purposes is to perturb all inputs simultaneously in an uncorrelated way. A drawback of this kind of excitation is that it may produce highly correlated outputs with a strong directionality, which is not good for identifiability. If this directionality is known, it can be counteracted by the input design. One method to do this was proposed twenty-five years ago. In this method, an estimate of the steady-state gain matrix is used to design inputs with the objective of obtaining outputs that are amplified equally in all directions. Design methods to include the effect of dynamics have recently been proposed. Although not included as a design criterion, the methods yield nearly uncorrelated outputs. Unfortunately, the methods are computationally very complicated. More recently, this author introduced a design method that directly addresses the output correlation. It is based on an approximate covariance model which allows the output correlation to be minimized by convex optimization techniques subject to variance constraints. In this paper, a more rigorous formulation using a full state-space model as well as a simplified formulation using an iteratively determined dynamic gain matrix are introduced. The usability of the three methods are illustrated by examples.