Prediction error identification of linear dynamic networks with rank-reduced noise

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of measured signals}, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramer-Rao lower bound in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in Automatica, 4 April 201

Learning linear modules in a dynamic network using regularized kernel-based methods

In order to identify one system (module) in an interconnected dynamic network, one typically has to solve a Multi-Input-Single-Output (MISO) identification problem that requires identification of all modules in the MISO setup. For application of a parametric identification method this would require estimating a large number of parameters, as well as an appropriate model order selection step for a possibly large scale MISO problem, thereby increasing the computational complexity of the identification algorithm to levels that are beyond feasibility. An alternative identification approach is presented employing regularized kernel-based methods. Keeping a parametric model for the module of interest, we model the impulse response of the remaining modules in the MISO structure as zero mean Gaussian processes (GP) with a covariance matrix (kernel) given by the first-order stable spline kernel, accounting for the noise model affecting the output of the target module and also for possible instability of systems in the MISO setup. Using an Empirical Bayes (EB) approach the target module parameters are estimated through an Expectation-Maximization (EM) algorithm with a substantially reduced computational complexity, while avoiding extensive model structure selection. Numerical simulations illustrate the potentials of the introduced method in comparison with the state-of-the-art techniques for local module identification.Comment: 15 pages, 7 figures, Submitted for publication in Automatica, 12 May 2020. Final version of paper submitted on 06 January 2021 (To appear in Automatica

Allocation of Excitation Signals for Generic Identifiability of Linear Dynamic Networks

A recent research direction in data-driven modeling is the identification of dynamic networks, in which measured vertex signals are interconnected by dynamic edges represented by causal linear transfer functions. The major question addressed in this paper is where to allocate external excitation signals such that a network model set becomes generically identifiable when measuring all vertex signals. To tackle this synthesis problem, a novel graph structure, referred to as \textit{directed pseudotree}, is introduced, and the generic identifiability of a network model set can be featured by a set of disjoint directed pseudotrees that cover all the parameterized edges of an \textit{extended graph}, which includes the correlation structure of the process noises. Thereby, an algorithmic procedure is devised, aiming to decompose the extended graph into a minimal number of disjoint pseudotrees, whose roots then provide the appropriate locations for excitation signals. Furthermore, the proposed approach can be adapted using the notion of \textit{anti-pseudotrees} to solve a dual problem, that is to select a minimal number of measurement signals for generic identifiability of the overall network, under the assumption that all the vertices are excited

Identification of systems with unknown inputs using indirect input measurements

A common issue with many system identification problems is that the true input to the system is unknown. This paper extends a previously presented indirect modelling framework that deals with identification of systems where the input is partially or fully unknown. In this framework, unknown inputs are eliminated by using additional measurements that directly or indirectly contain information about the unknown inputs. The resulting indirect predictor model is only dependent on known and measured signals and can be used to estimate the desired dynamics or properties. Since the input of the indirect model contains both known inputs and measurements that could all be correlated with the same disturbances as the output, estimation of the indirect model has similar challenges as a closed-loop estimation problem. In fact, due to the generality of the indirect modelling framework, it unifies a number of already existing system identification problems that are contained as special cases. For completeness, the paper is concluded with one method that can be used to estimate the indirect model as well as an experimental verification to show the applicability of the framework.Funding Agencies|Vinnova Industry Excellence Center LINK-SIC project [2007-02224]</p