arXiv subjects

Paul M. J. Van den Hof

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

At least 19 recordsLinked to original sources

arXiv2026

Data-informativity conditions for structured linear systems with implications for dynamic networks

When estimating a single subsystem (module) in a linear dynamic network with a prediction error method, a data-informativity condition needs to be satisfied for arriving at a consistent module estimate. This concerns a condition on input signals in the constructed, possibly MIMO (multiple input multiple output) predictor model being persistently exciting, which is typically guaranteed if the input spectrum is positive definite for a sufficient number of frequencies. Generically, the condition can be formulated as a path-based condition on the graph of the network model. The current condition has two elements of possible conservatism: (a) rather than focussing on the full MIMO model, one would like to be able to focus on consistently estimating the target module only, and (b) structural information, such as structural zero elements in the interconnection structure or known subsystems, should be taken into account. In this paper relaxed conditions for data-informativity are derived addressing these two issues, leading to relaxed path-based conditions on the network graph. This leads to experimental conditions that are less strict, i.e. require a smaller number of external excitation signals. Additionally, the new expressions for data-informativity in identification are shown to be closely related to earlier derived conditions for (generic) single module identifiability.

eess.SY↗

arXiv2026

Modelling and identification of diffusively coupled linear networks with additional directed links

Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows represent directions of information flow, thus a dynamic network can be visualised by a directed graph. In contrast, natural and physical laws only impose relations between systems variables, while variables are shared among systems via interconnections. Sharing is independent of direction, and therefore a dynamic network originating from physics can be visualised by an undirected graph. Typically, dynamic networks are considered to have either directed or undirected interconnections. For both situations, network models, analytic tools, and identification algorithms have been developed. However, dynamic networks can also have both directed and undirected interconnections, for example, in physical networks equipped with digital controllers. In this work, we present mixed linear dynamic networks that contain both undirected and directed interconnections, where the nature of the interconnecting dynamics needs to be incorporated into the modelling framework, identifiability analysis, and identification procedure. For these mixed networks, we derive dynamic network models; formulate conditions for consistent identification of all dynamics in the network; and develop a tractable identification algorithm that delivers consistent estimates.

eess.SY↗

arXiv2024

A frequency-domain approach for estimating continuous-time diffusively coupled linear networks

This paper addresses the problem of consistently estimating a continuous-time (CT) diffusively coupled network (DCN) to identify physical components in a physical network. We develop a three-step frequency-domain identification method for linear CT DCNs that allows to accurately recover all the physical component values of the network while exploiting the particular symmetric structure in a DCN model. This method uses the estimated noise covariance as a non-parametric noise model to minimize variance of the parameter estimates, obviating the need to select a parametric noise model. Moreover, this method is extended to subnetworks identification, which enables identifying the local dynamics in DCNs on the basis of partial measurements. The method is illustrated with an application from In-Circuit Testing of printed circuit boards. Experimental results highlight the method's ability to consistently estimate component values in a complex network with only a single excitation.

eess.SY↗

arXiv2024

Identifiability in Dynamic Acyclic Networks with Partial Excitations and Measurements

This paper deals with dynamic networks in which the causality relations between the vertex signals are represented by linear time-invariant transfer functions (modules). Considering an acyclic network where only a subset of its vertices are measured and a subset of the vertices are excited, we explore conditions under which all the modules are identifiable on the basis of measurement data. Two sufficient conditions are presented in the paper, where the first condition concerns an identifiability analysis that needs to be performed for each vertex, while the second condition, based on the concept of tree/anti-tree covering, results from a graphical synthesis approach to allocate actuators and sensors in an acyclic network for achieving generic identifiability.

math.OC↗

arXiv2023

On a Canonical Distributed Controller in the Behavioral Framework

Control in a classical transfer function or state-space setting typically views a controller as a signal processor: sensor outputs are mapped to actuator inputs. In behavioral system theory, control is simply viewed as interconnection; the interconnection of a plant with a controller. In this paper we consider the problem of control of interconnected systems in a behavioral setting. The behavioral setting is especially fit for modelling interconnected systems, because it allows for the interconnection of subsystems without imposing inputs and outputs. We introduce a so-called canonical distributed controller that implements a given interconnected behavior that is desired, provided that necessary and sufficient conditions hold true. The controller design can be performed in a decentralized manner, in the sense that a local controller only depends on the local system behavior. Regularity of interconnections is an important property in behavioral control that yields feedback interconnections. We provide conditions under which the interconnection of this distributed controller with the plant is regular. Furthermore, we show that the interconnections of subsystems of the canonical distributed controller are regular if and only if the interconnections of the plant and desired behavior are regular.

math.OC↗

arXiv2022

Learning linear modules in a dynamic network with missing node observations

In order to identify a system (module) embedded in a dynamic network, one has to formulate a multiple-input estimation problem that necessitates certain nodes to be measured and included as predictor inputs. However, some of these nodes may not be measurable in many practical cases due to sensor selection and placement issues. This may result in biased estimates of the target module. Furthermore, the identification problem associated with the multiple-input structure may require determining a large number of parameters that are not of particular interest to the experimenter, with increased computational complexity in large-sized networks. In this paper, we tackle these problems by using a data augmentation strategy that allows us to reconstruct the missing node measurements and increase the accuracy of the estimated target module. To this end, we develop a system identification method using regularized kernel-based methods coupled with approximate inference methods. Keeping a parametric model for the module of interest, we model the other modules as Gaussian Processes (GP) with a kernel given by the so-called stable spline kernel. An Empirical Bayes (EB) approach is used to estimate the parameters of the target module. The related optimization problem is solved using an Expectation-Maximization (EM) method, where we employ a Markov-chain Monte Carlo (MCMC) technique to reconstruct the unknown missing node information and the network dynamics. Numerical simulations on dynamic network examples illustrate the potentials of the developed method.

eess.SY↗

arXiv2022

Identification of diffusively coupled linear networks through structured polynomial models

Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric and therefore physical dynamic networks can be represented by undirected graphs. This paper shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the parameters and the interconnection structure of diffusively coupled networks. Further, a multi-step least squares convex optimization algorithm is developed to solve the nonconvex optimization problem that results from the identification method.

eess.SY↗

arXiv2022

A scalable multi-step least squares method for network identification with unknown disturbance topology

Identification methods for dynamic networks typically require prior knowledge of the network and disturbance topology, and often rely on solving poorly scalable non-convex optimization problems. While methods for estimating network topology are available in the literature, less attention has been paid to estimating the disturbance topology, i.e., the (spatial) noise correlation structure and the noise rank in a filtered white noise representation of the disturbance signal. In this work we present an identification method for dynamic networks, in which an estimation of the disturbance topology precedes the identification of the full dynamic network with known network topology. To this end we extend the multi-step Sequential Linear Regression and Weighted Null Space Fitting methods to deal with reduced rank noise, and use these methods to estimate the disturbance topology and the network dynamics in the full measurement situation. As a result, we provide a multi-step least squares algorithm with parallel computation capabilities and that rely only on explicit analytical solutions, thereby avoiding the usual non-convex optimizations involved. Consequently we consistently estimate dynamic networks of Box Jenkins model structure, while keeping the computational burden low. We provide a consistency proof that includes path-based data informativity conditions for allocation of excitation signals in the experimental design. Numerical simulations performed on a dynamic network with reduced rank noise clearly illustrate the potential of this method.

eess.SY↗

arXiv2022

On data-driven control: informativity of noisy input-output data with cross-covariance bounds

In this paper we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditions on the data. Informativity-conditions for stability, $\mathcal{H}_\infty$ and $\mathcal{H}_2$ control are developed, which are sufficient for input-output data and also necessary for input-state data. Simulation experiments illustrate that cross-covariance bounds can be less conservative for informativity, compared to norm bounds typically employed in the literature.

math.OC↗

arXiv2022

Informativity conditions for data-driven control based on input-state data and polyhedral cross-covariance noise bounds

Modeling and control of dynamical systems rely on measured data, which contains information about the system. Finite data measurements typically lead to a set of system models that are unfalsified, i.e., that explain the data. The problem of data-informativity for stabilization or control with quadratic performance is concerned with the existence of a controller that stabilizes all unfalsified systems or achieves a desired quadratic performance. Recent results in the literature provide informativity conditions for control based on input-state data and ellipsoidal noise bounds, such as energy or magnitude bounds. In this paper, we consider informativity of input-state data for control where noise bounds are defined through the cross-covariance of the noise with respect to an instrumental variable; bounds that were introduced originally as a noise characterization in parameter bounding identification. The considered cross-covariance bounds are defined by a finite number of hyperplanes, which induce a (possibly unbounded) polyhedral set of unfalsified systems. We provide informativity conditions for input-state data with polyhedral cross-covariance bounds for stabilization and $\mathcal{H}_2$/$\mathcal{H}_\infty$ control through vertex/half-space representations of the polyhedral set of unfalsified systems.

math.OC↗

arXiv2021

Single module identifiability in linear dynamic networks with partial excitation and measurement

Identifiability of a single module in a network of transfer functions is determined by whether a particular transfer function in the network can be uniquely distinguished within a network model set, on the basis of data. Whereas previous research has focused on the situations that all network signals are either excited or measured, we develop generalized analysis results for the situation of partial measurement and partial excitation. As identifiability conditions typically require a sufficient number of external excitation signals, this work introduces a novel network model structure such that excitation from unmeasured noise signals is included, which leads to less conservative identifiability conditions than relying on measured excitation signals only. More importantly, graphical conditions are developed to verify global and generic identifiability of a single module based on the topology of the dynamic network. Depending on whether the input or the output of the module can be measured, we present four identifiability conditions which cover all possible situations in single module identification. These conditions further lead to synthesis approaches for allocating excitation signals and selecting measured signals, to warrant single module identifiability. In addition, if the identifiability conditions are satisfied, indirect identification methods are developed to provide a consistent estimate of the module. All the obtained results are also extended to identifiability of multiple modules in the network.

eess.SY↗

arXiv2021

Generic identifiability of subnetworks in a linear dynamic network: the full measurement case

Identifiability conditions for single or multiple modules in a dynamic network specify under which conditions the considered modules can be uniquely recovered from the second-order statistical properties of the measured signals. Conditions for generic identifiability of multiple modules, i.e. a subnetwork, are developed for the situation that all node signals are measured and excitation of the network is provided by both measured excitation signals and unmeasured disturbance inputs. Additionally, the network model set is allowed to contain non-parametrized modules that are fixed, and e.g. reflect modules of which the dynamics are known to the user. The conditions take the form of path-based conditions on the graph of the network model set. Based on these conditions, synthesis results are formulated for allocating external excitation signals to achieve generic identifiability of particular subnetworks. If there are a sufficient number of measured external excitation signals, the formulated results give rise to a generalized indirect type of identification algorithm that requires only the measurement of a subset of the node signals in the network.

eess.SY↗

arXiv2021

A frequency domain approach for local module identification in dynamic networks

In classical approaches of dynamic network identification, in order to identify a system (module) embedded in a dynamic network, one has to formulate a Multi-input-Single-output (MISO) identification problem that requires identification of a parametric model for all the modules constituting the MISO setup including (possibly) the noise model, and determine their model order. This requirement leads to model order selection steps for modules that are of no interest to the experimenter which increases the computational complexity for large-sized networks. Also, identification using a parametric noise model (like BJ method) can suffer from local minima, however neglecting the noise model has its impact on the variance of the estimates. In this paper, we provide a two-step identification approach to avoid these problems. The first step involves performing a non-parametric indirect approach for a MISO identification problem to get the non-parametric frequency response function (FRF) estimates and its variance as a function of frequency. In the second step, the estimated non-parametric FRF of the target module is smoothed using a parametric frequency domain estimator with the estimated variance from the previous step as the non-parametric noise model. The developed approach is practical with weak assumptions on noise, uses the available toolbox, requires a parametric model only for the target module of interest, and uses a non-parametric noise model to reduce the variance of the estimates. Numerical simulations illustrate the potentials of the introduced method in comparison with the classical identification methods.

eess.SY↗

arXiv2021

A Necessary Condition for Network Identifiability with Partial Excitation and Measurement

This paper considers dynamic networks where vertices and edges represent manifest signals and causal dependencies among the signals, respectively. We address the problem of how to determine if the dynamics of a network can be identified when only partial vertices are measured and excited. A necessary condition for network identifiability is presented, where the analysis is performed based on identifying the dependency of a set of rational functions from excited vertices to measured ones. This condition is further characterised by using an edge-removal procedure on the associated bipartite graph. Moreover, on the basis of necessity analysis, we provide a necessary and sufficient condition for identifiability in circular networks.

math.OC↗

arXiv2021

Guaranteed $\mathcal{H}_\infty$ performance analysis and controller synthesis for interconnected linear systems from noisy input-state data

The increase in available data and complexity of dynamical systems has sparked the research on data-based system performance analysis and controller design. Recent approaches can guarantee performance and robust controller synthesis based on noisy input-state data of a single dynamical system. In this paper, we extend a recent data-based approach for guaranteed performance analysis to distributed analysis of interconnected linear systems. We present a new set of sufficient LMI conditions based on noisy input-state data that guarantees $\mathcal{H}_\infty$ performance and have a structure that lends itself well to distributed controller synthesis from data. Sufficient LMI conditions based on noisy data are provided for the existence of a dynamic distributed controller that achieves $\mathcal{H}_\infty$ performance. The presented approach enables scalable analysis and control of large-scale interconnected systems from noisy input-state data sets.

eess.SY↗

arXiv2021

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.

math.OC↗

arXiv2021

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.

eess.SY↗

arXiv2021

Scalable distributed and decentralized $\mathscr{H}_2$ controller synthesis for interconnected linear discrete-time systems

The current limitation in the synthesis of distributed $\mathscr{H}_2$ controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed $\mathscr{H}_2$ controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complexity compared to the corresponding centralized $\mathscr{H}_2$ controller synthesis problem. Additionally, the developed conditions are adapted for the corresponding decentralized $\mathscr{H}_2$ controller synthesis problem with fixed supply functions for the interconnections. The effectiveness and scalability of the developed distributed $\mathscr{H}_2$ controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph.

eess.SY↗