Closed-loop identification of MIMO systems: a new look at identifiability and experiment design

This paper addresses a question raised by a leading expert in the identification of multivariable systems: “Is it necessary to excite all reference signals for the identification of a multivariable system operating in closed loop with a linear time-invariant controller?” On the basis of earlier results on identifiability of closed-loop systems, he conjectured that this was necessary. We show that it is not, on the basis of a careful re-examination of the notions of identifiability and informative experiments for closed-loop systems

Informative data: how to get just sufficiently rich?

Prediction error identification requires that data be informative with respect to the chosen model structure. Whereas sufficient conditions for informative experiments have been available for a long time, there were surprisingly no results of necessary and sufficient nature. With the recent surge of interest in optimal experiment design, it is of interest to know the minimal richness required of the externally applied signal to make the experiment informative. We provide necessary and sufficient conditions on the degree of richness of the applied signal to generate an informative experiment, both in open loop and in closed loop. In a closed-loop setup, where identification can be achieved with no external excitation if the controller is of sufficient degree, our results provide a precisely quantifiable trade-off between controller degree and required degree of external excitation

On the shape of H2 performance criteria

An H2 control performance criterion dependent on a controller parameter vector is analyzed from the point of view of evaluating the domain of attraction of its global minimum when a gradient-based algorithm is used in tuning the parameters. The objective of this analysis is twofold: (i) examine how some design parameters of the criterion can be used to enlarge the domain of attraction; (ii) examine how the minimization of a sequence of intermediate criteria can possibly lead to the global minimum of the original criterion without the danger of entrapment in a local minimum