Data Informativity for the Identication of particular Parallel Hammerstein Systems

To obtain a consistent estimate when performing an identication with Prediction Error, it is important that the excitation yields informative data with respect to the chosen model structure. While the characterization of this property seems to be a mature research area in the linear case, the same cannot be said for nonlinear systems. In this work, we study the data informativity for a particular type of Hammerstein systems for two commonly-used excitations: white Gaussian noise and multisine. The real life example of the MEMS gyroscope is considered

Data Informativity for the Identication of MISO FIR Systems with Filtered White Noise Excitation

For Prediction Error Identication, there are two main ingredients to get a consistent estimate: one of them is the data informativity with respect to (w.r.t.) the considered model structure. One common criterion used for the informativity is the positive deniteness of the input density spectral power (DSP) matrix at all frequencies. This criterion is not appropriate for multisine excitation but can be used for ltered white noise excitation for many identication problems. However, this criterion is not necessary and its application for some identication problems might not be possible. In this paper, we propose a necessary and sucient condition for the data informativity in the case of multiple-inputs single-output (MISO) nite impulse response (FIR) model structure in open-loop

Informativity: how to get just sufficiently rich for the Identification of MISO FIR Systems with Multisine Excitation?

In Prediction Error Identification, the consistency of the identified parameter vector is only guaranteed if the data are informative enough i.e. if the excitation signal is sufficiently rich. For single-input single-output systems, one can verify whether a given excitation is sufficiently rich for a system based on the number of frequencies at which its power spectrum is nonzero. The extension of this criterion to multivariate systems is not straightforward. In the literature, one has proposed criteria based on the number of frequencies at which the power spectrum matrix of the excitation signal is strictly positive definite. However, this criterion is too restrictive as it does not cover the case of multisine excitations, while it is well known that such excitation signals can lead to consistent estimates. This paper proposes less restrictive conditions for the consistency of the identified parameter vector when FIR multiple-inputs single-output systems have to be identified with multisine signals in the open loop configuration

Data Informativity for the Open-Loop Identification of MIMO Systems in the Prediction Error Framework

In Prediction Error identification, to obtain a consistent estimate of the true system, it is crucial that the input excitation yields informative data with respect to the chosen model structure. We consider in this paper the data informativity property for the identification of a Multiple-Input Multiple-Output system in open loop and we derive conditions to check whether a given input vector will yield informative data with respect to the chosen model structure. We do that for the classical model structures used in prediction-error identification and for the classical types of input vectors, i.e., input vectors whose elements are either multisines or filtered white noises

Closed-loop Identification of MIMO Systems in the Prediction Error Framework: Data Informativity Analysis

In the Prediction Error Identification framework, it is essential that the experiment yields informative data with respect to the chosen model structure to get a consistent estimate. In this work, we focus on the data informativity property for the identification of Multi-Inputs Multi-Outputs system in closed-loop and we derive conditions to verify if a given external excitation combined with the feedback introduced by the controller yields informative data with respect to the model structure. This study covers the case of the classical model structures used in prediction-error identification and the classical types of external excitation vectors, i.e., vectors whose elements are either multisine or filtered white noises

Optimal Experiment Design for the Identification of One Module in the Interconnection of Locally Controlled Systems

International audienceIn this paper, we consider the problem of designing the least costly experiment that leads to a sufficiently accurate estimate of one module in a network of locally controlled systems. A module in such a network can be identified by exciting the corresponding local closed loop system. Such an excitation signal will not only perturb the input/output of the to-be-identified module, but also other modules due to the interconnection. Consequently, the cost of the identification can be expressed as the sum of the influence of the excitation signal on the inputs and outputs of all locally controlled systems. We develop a methodology to design the spectrum of the excitation signal in such a way that this cost is minimized while guaranteeing a certain accuracy for the identified model. We also propose an alternative identification configuration which can further reduce the propagation of the excitation signal to other modules and we make steps to robustify this optimal experiment design problem with respect to the cost of the identification

Robust optimal identification experiment design for multisine excitation

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. 1 Introduction We consider in this paper the problem of optimally designing the spectrum Φ u of the excitation signal u of an open-loop identification experiment. By optimal spectrum , we here mean the spectrum yielding the smallest experiment cost while guaranteeing that the accuracy of the identified parameter vector of the plant transfer function is larger than a given threshold. We thus consider the least costly experiment design framework [5], but the approach can easily be adapted to other (dual) frameworks [10,17,13]. The experiment cost J can be defined as a linear combination of the power of the exci-tation signal u and of the power of the part of the output signal induced by u. The experiment cost will therefore be a function of the spectrum Φ u , but also of the unknown true parameter vector θ 0 (we therefore denote the cost as J (θ 0 , Φ u)). Likewise, the accuracy constraint will also depend on θ 0 and on Φ u since the classical accuracy constraints are of the type P −1 (θ 0 , Φ u) ≥ R adm where P (θ 0 , Φ u) is the covariance matrix of the to-be-identified parameter vector (which depends on θ 0 and Φ u) and R adm a matrix reflecting the desired accuracy. The dependency of the optimal spectrum Φ u,opt on the unknown true parameter vector θ 0 is the so-called chicken-and-egg issue encountered in optimal experiment design. This issue is generally circumvented by replacing θ 0 b

Growing in time IDLA cluster is recurrent

We show that Internal Diffusion Limited Aggregation (IDLA) on $\mathbb{Z}^d$ has near optimal Cheeger constant when the growing cluster is large enough. This implies, through a heat kernel lower bound derived previously in [H], that simple random walk evolving independently on growing in time IDLA cluster is recurrent when $d\ge 3$

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

In this paper we consider the design of the least costly experiment for the identification of one module in a given network of locally controlled systems. The identification experiment will be designed in such a way that we obtain a sufficiently accurate model of the to-be-identified module with the smallest identification cost i.e. with the least perturbation of the network

Atomic Analysis of Protein-Protein Interfaces with Known Inhibitors: The 2P2I Database

BACKGROUND: In the last decade, the inhibition of protein-protein interactions (PPIs) has emerged from both academic and private research as a new way to modulate the activity of proteins. Inhibitors of these original interactions are certainly the next generation of highly innovative drugs that will reach the market in the next decade. However, in silico design of such compounds still remains challenging. METHODOLOGY/PRINCIPAL FINDINGS: Here we describe this particular PPI chemical space through the presentation of 2P2I(DB), a hand-curated database dedicated to the structure of PPIs with known inhibitors. We have analyzed protein/protein and protein/inhibitor interfaces in terms of geometrical parameters, atom and residue properties, buried accessible surface area and other biophysical parameters. The interfaces found in 2P2I(DB) were then compared to those of representative datasets of heterodimeric complexes. We propose a new classification of PPIs with known inhibitors into two classes depending on the number of segments present at the interface and corresponding to either a single secondary structure element or to a more globular interacting domain. 2P2I(DB) complexes share global shape properties with standard transient heterodimer complexes, but their accessible surface areas are significantly smaller. No major conformational changes are seen between the different states of the proteins. The interfaces are more hydrophobic than general PPI's interfaces, with less charged residues and more non-polar atoms. Finally, fifty percent of the complexes in the 2P2I(DB) dataset possess more hydrogen bonds than typical protein-protein complexes. Potential areas of study for the future are proposed, which include a new classification system consisting of specific families and the identification of PPI targets with high druggability potential based on key descriptors of the interaction. CONCLUSIONS: 2P2I database stores structural information about PPIs with known inhibitors and provides a useful tool for biologists to assess the potential druggability of their interfaces. The database can be accessed at http://2p2idb.cnrs-mrs.fr