arXiv subjects

Paul M. J. Van den Hof

Publications and source records attributed to Paul M. J. Van den Hof.

32 records · Page 2Linked to original sources

arXiv2020

A local direct method for module identification in dynamic networks with correlated noise

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is a set of algorithms that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. Three algorithms are presented that differ in their approach of selecting measured node signals. Either a maximum or a minimum number of measured node signals can be considered, as well as a preselected set of measured nodes.

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arXiv2020

Data-driven distributed control: Virtual reference feedback tuning in dynamic networks

In this paper, the problem of synthesizing a distributed controller from data is considered, with the objective to optimize a model-reference control criterion. We establish an explicit ideal distributed controller that solves the model-reference control problem for a structured reference model. On the basis of input-output data collected from the interconnected system, a virtual experiment setup is constructed which leads to a network identification problem. We formulate a prediction-error identification criterion that has the same global optimum as the model-reference criterion, when the controller class contains the ideal distributed controller. The developed distributed controller synthesis method is illustrated on an academic example network of nine subsystems and the influence of the controller interconnection structure on the achieved closed-loop performance is analyzed.

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arXiv2020

A Bayesian method for inference of effective connectivity in brain networks for detecting the Mozart effect

Several studies claim that listening to Mozart music affects cognition and can be used to treat neurological conditions like epilepsy. Research into this Mozart effect has not addressed how dynamic interactions between brain networks, i.e. effective connectivity, are affected. The Granger-causality analysis is often used to infer effective connectivity. First, we investigate if a new method, Bayesian topology identification, can be used as an alternative. Both methods are evaluated on simulation data, where the Bayesian method outperforms the Granger-causality analysis in the inference of connectivity graphs of dynamic networks, especially for short data lengths. In the second part, the Bayesian method is extended to enable the inference of changes in effective connectivity between groups of subjects. Next, we apply both methods to fMRI scans of 16 healthy subjects, who were scanned before and after exposure to Mozart's sonata K448 at least 2 hours a day for 7 days. Here, we investigate if the effective connectivity of the subjects significantly changed after listening to Mozart music. The Bayesian method detected changes in effective connectivity between networks related to cognitive processing and control: First, in the connection from the central executive to the superior sensori-motor network. Second, in the connection from the posterior default mode to the fronto-parietal right network. Finally, in the connection from the anterior default mode to the dorsal attention network, but only in a subgroup of subjects with a longer listening duration. Only in this last connection an effect was found by the Granger-causality analysis.

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arXiv2020

Abstractions of linear dynamic networks for input selection in local module identification

In abstractions of linear dynamic networks, selected node signals are removed from the network, while keeping the remaining node signals invariant. The topology and link dynamics, or modules, of an abstracted network will generally be changed compared to the original network. Abstractions of dynamic networks can be used to select an appropriate set of node signals that are to be measured, on the basis of which a particular local module can be estimated. A method is introduced for network abstraction that generalizes previously introduced algorithms, as e.g. immersion and the method of indirect inputs. For this abstraction method it is shown under which conditions on the selected signals a particular module will remain invariant. This leads to sets of conditions on selected measured node variables that allow identification of the target module.

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arXiv2019

Local module identification in dynamic networks with correlated noise: the full input case

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, typically under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is an algorithm that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. As a first step in the analysis, we restrict attention to the (slightly conservative) situation where the selected output node signals are predicted based on all of their in-neighbor node signals in the network.

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arXiv2019

Bayesian topology identification of linear dynamic networks

In networks of dynamic systems, one challenge is to identify the interconnection structure on the basis of measured signals. Inspired by a Bayesian approach in [1], in this paper, we explore a Bayesian model selection method for identifying the connectivity of networks of transfer functions, without the need to estimate the dynamics. The algorithm employs a Bayesian measure and a forward-backward search algorithm. To obtain the Bayesian measure, the impulse responses of network modules are modeled as Gaussian processes and the hyperparameters are estimated by marginal likelihood maximization using the expectation-maximization algorithm. Numerical results demonstrate the effectiveness of this method.

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arXiv2018

A recursive estimation approach to distributed identification of large-scale multi-input-single-output FIR systems

The problem of identifying single modules in multiple-input-single-output (MISO) systems is considered. A novel approach to distributed identification of MISO finite impulse response systems is presented. The distributed identification is discerned by the local estimation of local parameters, which correspond to a module in the MISO system. The local estimators are derived from the standard recursive least squares estimator and require limited information exchange. By Lyapunov's second method, sufficient conditions are derived for asymptotic convergence of the estimators to the true parameters in the absence of disturbances, which lead to asymptotic unbiasedness in the presence of additive output disturbances.

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arXiv2018

Local module identification in dynamic networks: do more inputs guarantee smaller variance?

Recent developments in science and engineering have motivated control systems to be considered as interconnected and networked systems. From a system identification point of view, modelling of a local module in such a structured system is a relevant and interesting problem. This work focuses on the quality, in terms of variance, of an estimate of a local module. We analyse which predictor input signals are relevant and contribute to variance reduction, while still guaranteeing the consistency of the estimate. For a targeted local module, a comparison of its estimate variance is made between a full-MISO approach and an immersed network setting, where a reduced number of inputs is used, while still guaranteeing consistency. A case study of a four-node network is considered and it is shown that a smaller set of predictor inputs can, under some conditions, result in a smaller variance compared to the full-MISO approach.

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arXiv2018

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.

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arXiv2018

Single module identifiability in linear dynamic networks

A recent development in data-driven modelling addresses the problem of identifying dynamic models of interconnected systems, represented as linear dynamic networks. For these networks the notion network identifiability has been introduced recently, which reflects the property that different network models can be distinguished from each other. Network identifiability is extended to cover the uniqueness of a single module in the network model. Conditions for single module identifiability are derived and formulated in terms of path-based topological properties of the network models.

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arXiv2017

Identifiability of linear dynamic networks

Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we need to make sure that the network model set is identifiable. We introduce the notion of network identifiability, as a property of a parameterized model set, that ensures that different network models can be distinguished from each other when performing identification on the basis of measured data. Different from the classical notion of (parameter) identifiability, we focus on the distinction between network models in terms of their transfer functions. For a given structured model set with a pre-chosen topology, identifiability typically requires conditions on the presence and location of excitation signals, and on presence, location and correlation of disturbance signals. Because in a dynamic network, disturbances cannot always be considered to be of full-rank, the reduced-rank situation is also covered, meaning that the number of driving white noise processes can be strictly less than the number of disturbance variables. This includes the situation of having noise-free nodes.

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arXiv2017

Identification in Dynamic Networks

System identification is a common tool for estimating (linear) plant models as a basis for model-based predictive control and optimization. The current challenges in process industry, however, ask for data-driven modelling techniques that go beyond the single unit/plant models. While optimization and control problems become more and more structured in the form of decentralized and/or distributed solutions, the related modelling problems will need to address structured and interconnected systems. An introduction will be given to the current state of the art and related developments in the identification of linear dynamic networks. Starting from classical prediction error methods for open-loop and closed-loop systems, several consequences for the handling of network situations will be presented and new research questions will be highlighted.

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arXiv2015

Observer-based correct-by-design controller synthesis

Current state-of-the-art correct-by-design controllers are designed for full-state measurable systems. This work first extends the applicability of correct-by-design controllers to partially observable LTI systems. Leveraging 2nd order bounds we give a design method that has a quantifiable robustness to probabilistic disturbances on state transitions and on output measurements. In a case study from smart buildings we evaluate the new output-based correct-by-design controller on a physical system with limited sensor information.

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arXiv2015

Data-driven and Model-based Verification: a Bayesian Identification Approach

This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to compute the confidence that a physical system driven by external inputs and accessed under noisy measurements, verifies a temporal logic property. A case study is discussed, where we investigate the bounded- and unbounded-time safety of a partly unknown linear time invariant system.

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