Robust optimal identification experiment design for multisine excitation

Abstract

In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal.

Least costly identification experiment for the identification of one module in a dynamic network

“…We suppose that M is globally identifiable at θ 0,l i.e., θ l = θ 0,l is the only parameter vector for which G l (z, θ l ) and H l (z, θ l ) corresponds to S l . We will also suppose that the excitation signal r(t) (see Figure 3) and the white noise vectorē (see (3)) are uncorrelated and that ref ext (t) is a stationary signal uncorrelated with r(t) andē(t). Then, using the data set {y l (t), u l (t)|t = 1, .…”

“…For this purpose, as we will see in the sequel, we will need to consider an optimal experiment design where the cost constraint is robustified with respect to the initial uncertainty of the initial estimate. In [3], we have recentlty proposed an approach to tackle such a robustified cost constraint. With respect to the earlier approaches for this problem [27,20,10], the approach in [3] does not entail any kind of approximation.…”

“…In [3], we have recentlty proposed an approach to tackle such a robustified cost constraint. With respect to the earlier approaches for this problem [27,20,10], the approach in [3] does not entail any kind of approximation. However, the possible high dimension of the network can imply an excessive computational complexity for the approach in [3].…”

“…With respect to the earlier approaches for this problem [27,20,10], the approach in [3] does not entail any kind of approximation. However, the possible high dimension of the network can imply an excessive computational complexity for the approach in [3]. To avoid this problem, we propose in this paper an alternative approach which is more appropriate to the network situation (and its possible high dimension) and which, while being (slightly) more conservative, has the same property as the one in [3] i.e., it is not based on any approximation.…”

“…However, the possible high dimension of the network can imply an excessive computational complexity for the approach in [3]. To avoid this problem, we propose in this paper an alternative approach which is more appropriate to the network situation (and its possible high dimension) and which, while being (slightly) more conservative, has the same property as the one in [3] i.e., it is not based on any approximation. This absence of approximation is also the main difference with the approach proposed in the conference paper [24] on which the present paper is based.…”