arXiv subjects

Luis A. Aguirre

Publications and source records attributed to Luis A. Aguirre.

15 recordsLinked to original sources

arXiv2026

Experimental Kuramoto Platform

Phase reduction provides a principled relationship between high-dimensional oscillator dynamics and low-dimensional phase models such as the Kuramoto model. However, connecting analytical results derived from the Kuramoto framework to experimental data remains an open challenge, as many physical platforms violate the weak-coupling assumptions underlying standard phase reduction. Here, we present an experimental platform based on electronic quadrature oscillators whose phase dynamics are, under certain assumptions, equivalent to the Kuramoto model. Crucially, this equivalence is achieved for both weak and strong coupling through a non-diffusive coupling circuit, and the design approach supports arbitrary (weighted and directed) network topologies while preserving scalability and oscillation regularity. Across different coupling schemes, we demonstrate that the platform reliably reproduces phase transitions predicted by the Kuramoto model for both global and cluster synchronization. This cost-effective platform enables systematic experimental validation of analytical and numerical results for synchronization in complex networks.

cond-mat.stat-mech↗

arXiv2022

Functional observability and target state estimation in large-scale networks

The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or physically impossible to have enough sensor nodes to make the system fully observable. Even if the system is in principle observable, high-dimensionality poses fundamental limits on the computational tractability and performance of a full-state observer. To overcome the curse of dimensionality, we instead require the system to be functionally observable, meaning that a targeted subset of state variables can be reconstructed from the available measurements. Here, we develop a graph-based theory of functional observability, which leads to highly scalable algorithms to i) determine the minimal set of required sensors and ii) design the corresponding state observer of minimum order. Compared to the full-state observer, the proposed functional observer achieves the same estimation quality with substantially less sensing and computational resources, making it suitable for large-scale networks. We apply the proposed methods to the detection of cyber-attacks in power grids from limited phase measurement data and the inference of the prevalence rate of infection during an epidemic under limited testing conditions. The applications demonstrate that the functional observer can significantly scale up our ability to explore otherwise inaccessible dynamical processes on complex networks.

eess.SY↗

arXiv2021

Identification of NARX Models for Compensation Design

This report presents the modeling results for three systems, two numerical and one experimental. In the numerical examples, we use mathematical models previously obtained in the literature as the systems to be identified. The first numerical example is a heating system with a polynomial nonlinearity that is described by a Hammerstein model. The second is a Bouc-Wen model that represents the hysteretic behavior in a piezoelectric actuator. Finally, the experimental example is a pneumatic valve that presents a variety of nonlinearities, including hysteresis. For each example, a Nonlinear AutoRegressive model with eXogenous inputs (NARX) is identified using two well-established techniques together, the Error Reduction Ratio (ERR) method to hierarchically select the regressors and the Akaike's Information Criterion (AIC) to truncate the number of terms. Using both approaches, the structure selection is achieved. The design of the excitation input is based on preserving the frequencies of interest and force the system to achieve different points of operation. Hence, having the structure previously selected with ERR and AIC, we use the Extended Least Squares (ELS) algorithm to estimate the parameters. The results show that it is possible to identify the referred systems with no more than five terms. These identified models will be used for nonlinearity compensation in future works.

eess.SY↗

arXiv2020

Nonlinearity Compensation Based on Identified NARX Polynomials Models

This paper deals with the compensation of nonlinearities in dynamical systems using nonlinear polynomial autoregressive models with exogenous inputs (NARX). The compensation approach is formulated for static and dynamical contexts, as well as its adaptation to hysteretic systems. In all of these scenarios, identified NARX models are used. The core idea is to rewrite the model as an algebraic polynomial whose roots are potential compensation inputs. A procedure is put forward to choose the most adequate root, in cases where more than one is possible. Both numerical and experimental results are presented to illustrate the method. In the experimental case the method is compared to other approaches. The results show that the proposed methodology can provide compensation input signals that practically linearize the studied systems using simple and representative models with no more than five terms.

eess.SY↗

arXiv2020

Including steady-state information in nonlinear models: an application to the development of soft-sensors

When the dynamical data of a system only convey dynamic information over a limited operating range, the identification of models with good performance over a wider operating range is very unlikely. Nevertheless, models with such characteristic are desirable to implement modern control systems. To overcome such a shortcoming, this paper describes a methodology to train models from dynamical data and steady-state information, which is assumed available. The novelty is that the procedure can be applied to models with rather complex structures such as multilayer perceptron neural networks in a bi-objective fashion without the need to compute fixed points neither analytically nor numerically. As a consequence, the required computing time is greatly reduced. The capabilities of the proposed method are explored in numerical examples and the development of soft-sensors for downhole pressure estimation for a real deep-water offshore oil well. The results indicate that the procedure yields suitable soft-sensors with good dynamical and static performance and, in the case of models that are nonlinear in the parameters, the gain in computation time is about three orders of magnitude considering existing approaches.

eess.SY↗

arXiv2020

On the smoothness of nonlinear system identification

We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the Lipschitz constant and $β$-smoothness of the objective function might blow up exponentially with the simulation length, making it hard to numerically find minima within those regions or, even, to escape from them. In addition to providing theoretical understanding of this problem, this paper also proposes the use of multiple shooting as a viable solution. The proposed method minimizes the error between a prediction model and the observed values. Rather than running the prediction model over the entire dataset, multiple shooting splits the data into smaller subsets and runs the prediction model over each subset, making the simulation length a design parameter and making it possible to solve problems that would be infeasible using a standard approach. The equivalence to the original problem is obtained by including constraints in the optimization. The new method is illustrated by estimating the parameters of nonlinear systems with chaotic or unstable behavior, as well as neural networks. We also present a comparative analysis of the proposed method with multi-step-ahead prediction error minimization.

eess.SY↗

arXiv2020

Beyond exploding and vanishing gradients: analysing RNN training using attractors and smoothness

The exploding and vanishing gradient problem has been the major conceptual principle behind most architecture and training improvements in recurrent neural networks (RNNs) during the last decade. In this paper, we argue that this principle, while powerful, might need some refinement to explain recent developments. We refine the concept of exploding gradients by reformulating the problem in terms of the cost function smoothness, which gives insight into higher-order derivatives and the existence of regions with many close local minima. We also clarify the distinction between vanishing gradients and the need for the RNN to learn attractors to fully use its expressive power. Through the lens of these refinements, we shed new light on recent developments in the RNN field, namely stable RNN and unitary (or orthogonal) RNNs.

cs.LG↗

arXiv2020

Identification and nonlinearity compensation of hysteresis using NARX models

This paper deals with two problems: the identification and compensation of hysteresis nonlinearity in dynamical systems using nonlinear polynomial autoregressive models with exogenous inputs (NARX). First, based on gray-box identification techniques, some constraints on the structure and parameters of NARX models are proposed to ensure that the identified models display a key-feature of hysteresis. In addition, a more general framework is developed to explain how hysteresis occurs in such models. Second, two strategies to design hysteresis compensators are presented. In one strategy the compensation law is obtained through simple algebraic manipulations performed on the identified models. It has been found that the compensators based on gray-box models outperform the cases with models identified using black-box techniques. In the second strategy, the compensation law is directly identified from the data. Both numerical and experimental results are presented to illustrate the efficiency of the proposed procedures.

eess.SY↗

arXiv2018

Particle filtering of dynamical networks: Highlighting observability issues

In a network of high-dimensionality, it is not feasible to measure every single node. Thus, an important goal in the literature is to define the optimal choice of sensor nodes that provides a reliable state reconstruction of the network system state-space. This is an observability problem. In this paper, we propose a particle filtering (PF) framework as a way to assess observability properties of a dynamical network, where each node is composed by an individual dynamical system. The PF framework is applied on two benchmarks, networks of Kuramoto and Rössler oscillators, to investigate how the interplay between dynamics and topology impacts the network observability. Based on the numerical results, we conjecture that, when the network nodal dynamics are heterogeneous, better observability is conveyed for sets of sensor nodes that share some dynamical affinity to its neighbourhood. Moreover, we also investigate how the choice of an internal measured variable of a multidimensional sensor node affects the PF performance. The PF framework effectiveness as an observability measure is compared to a well-consolidated nonlinear observability metric for a small network case and some chaotic systems benchmarks.

nlin.CD↗

arXiv2018

"Parallel Training Considered Harmful?": Comparing series-parallel and parallel feedforward network training

Neural network models for dynamic systems can be trained either in parallel or in series-parallel configurations. Influenced by early arguments, several papers justify the choice of series-parallel rather than parallel configuration claiming it has a lower computational cost, better stability properties during training and provides more accurate results. Other published results, on the other hand, defend parallel training as being more robust and capable of yielding more accu- rate long-term predictions. The main contribution of this paper is to present a study comparing both methods under the same unified framework. We focus on three aspects: i) robustness of the estimation in the presence of noise; ii) computational cost; and, iii) convergence. A unifying mathematical framework and simulation studies show situations where each training method provides better validation results, being parallel training better in what is believed to be more realistic scenarios. An example using measured data seems to reinforce such claim. We also show, with a novel complexity analysis and numerical examples, that both methods have similar computational cost, being series series-parallel training, however, more amenable to parallelization. Some informal discussion about stability and convergence properties is presented and explored in the examples.

eess.SY↗

arXiv2018

Structural, Dynamical and Symbolic Observability: From Dynamical Systems to Networks

The concept of observability of linear systems initiated with Kalman in the mid 1950s. Roughly a decade later, the observability of nonlinear systems appeared. By such definitions a system is either observable or not. Continuous measures of observability for linear systems were proposed in the 1970s and two decades ago were adapted to deal with nonlinear dynamical systems. Related topics developed either independently or as a consequence of these. Observability has been recognized as an important feature to study complex networks, but as for dynamical systems in the beginning the focus has been on determining conditions for a network to be observable. In this relatively new field previous and new results on observability merge either producing new terminology or using terms, with well established meaning in other fields, to refer to new concepts. Motivated by the fact that twenty years have passed since some of these concepts were introduced in the field of nonlinear dynamics, in this paper (i)~various aspects of observability will be reviewed, and (ii)~it will be discussed in which ways networks could be ranked in terms of observability. The aim is to make a clear distinction between concepts and to understand what does each one contribute to the analysis and monitoring of networks. Some of the main ideas are illustrated with simulations.

nlin.CD↗

arXiv2018

A nonlinear graph-based theory for dynamical network observability

A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high dimensional dynamics. However, even if the network dynamics is observable from a reduced set of measured variables, how to reliably identifying such a minimum set of variables providing full observability remains an unsolved problem. From the Jacobian matrix of the governing equations of nonlinear systems, we construct a {\it pruned fluence graph} in which the nodes are the state variables and the links represent {\it only the linear} dynamical interdependences encoded in the Jacobian matrix after ignoring nonlinear relationships. From this graph, we identify the largest connected sub-graphs where there is a path from every node to every other node and there are not outcoming links. In each one of those sub-graphs, at least one node must be measured to correctly monitor the state of the system in a $d$-dimensional reconstructed space. Our procedure is here validated by investigating large-dimensional reaction networks for which the determinant of the observability matrix can be rigorously computed.

nlin.CD↗

arXiv2018

Lasso Regularization Paths for NARMAX Models via Coordinate Descent

We propose a new algorithm for estimating NARMAX models with $L_1$ regularization for models represented as a linear combination of basis functions. Due to the $L_1$-norm penalty the Lasso estimation tends to produce some coefficients that are exactly zero and hence gives interpretable models. The novelty of the contribution is the inclusion of error regressors in the Lasso estimation (which yields a nonlinear regression problem). The proposed algorithm uses cyclical coordinate descent to compute the parameters of the NARMAX models for the entire regularization path. It deals with the error terms by updating the regressor matrix along with the parameter vector. In comparative timings we find that the modification does not reduce the computational efficiency of the original algorithm and can provide the most important regressors in very few inexpensive iterations. The method is illustrated for linear and polynomial models by means of two examples.

eess.SY↗

arXiv2017

Mixed measurements and the detection of phase synchronization in networks

Multivariate singular spectrum analysis (M-SSA), with a varimax rotation of eigenvectors, was recently proposed to provide detailed information about phase synchronization in networks of nonlinear oscillators without any a priori need for phase estimation. The discriminatory power of M-SSA is often enhanced by using only the time series of the variable that provides the best observability of the node dynamics. In practice, however, diverse factors could prevent one to have access to this variable in some nodes and other variables should be used, resulting in a mixed set of variables. In the present work, the impact of this mixed measurement approach on the M-SSA is numerically investigated in networks of Rössler systems and cord oscillators. The results are threefold. First, a node measured by a poor variable, in terms of observability, becomes virtually invisible to the technique. Second, a side effect of using a poor variable is that the characterization of phase synchronization clustering of the {\it other}\, nodes is hindered by a small amount. This suggests that, given a network, synchronization analysis with M-SSA could be more reliable by not measuring those nodes that are accessible only through poor variables. Third, global phase synchronization could be detected even using only poor variables, given enough of them are measured. These insights could be useful in defining measurement strategies for both experimental design and real world applications for use with M-SSA.

nlin.CD↗

arXiv2017

Observability and Synchronization of Neuron Models

Observability is the property that enables to distinguish two different locations in $n$-dimensional state space from a reduced number of measured variables, usually just one. In high-dimensional systems it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. In the case of networks composed of neuron models, the observability of the network depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, a study of observability is conducted using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, a multivariate singular spectrum analysis (M-SSA) is performed to detect phase synchronization in networks composed by neuron models. This tool, to the best of the authors' knowledge has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization i)~without having to measure all the state variables, but only one from each node, and ii)~without having to estimate the phase.

q-bio.NC↗