arXiv subjects

Constantino M. Lagoa

Publications and source records attributed to Constantino M. Lagoa.

16 recordsLinked to original sources

arXiv2026

RAIN-FIT: Learning of Fitting Surfaces and Noise Distribution from Large Data Sets

This paper proposes a method for estimating a surface that contains a given set of points from noisy measurements. More precisely, by assuming that the surface is described by the zero set of a function in the span of a given set of features and a parametric description of the distribution of the noise, a computationally efficient method is described that estimates both the surface and the noise distribution parameters. In the provided examples, polynomial and sinusoidal basis functions were used. However, any chosen basis that satisfies the outlined conditions mentioned in the paper can be approximated as a combination of trigonometric, exponential, and/or polynomial terms, making the presented approach highly generalizable. The proposed algorithm exhibits linear computational complexity in the number of samples. Our approach requires no hyperparameter tuning or data preprocessing and effectively handles data in dimensions beyond 2D and 3D. The theoretical results demonstrating the convergence of the proposed algorithm have been provided. To highlight the performance of the proposed method, comprehensive numerical results are conducted, evaluating our method against state-of-the-art algorithms, including Poisson Reconstruction and the Neural Network-based Encoder-X, on 2D and 3D shapes. The results demonstrate the superiority of our method under the same conditions.

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arXiv2026

A Dynamic Phasor Framework for Analysis of Subsynchronous Oscillations in Multi-Machine Systems with IBRs and Large Loads

Although the electromagnetic transient (EMT) framework can capture subsynchronous oscillations (SSOs), it faces scalability issues for large-scale systems. Thus motivated, we propose a generalized dynamic phasor (DP) framework to analyze SSOs in multi-machine systems with inverter-based resources (IBRs) and large loads such as artificial intelligence data centers (AI DCs) under balanced and unbalanced conditions. The grid-following (GFL) and grid-forming (GFM) IBRs are modeled in their respective $dq$-frame DPs. In contrast, the detailed model of multi-mass turbine driven synchronous generators (SGs) along with dynamic transmission network models and loads are represented in $pnz$-frame DPs. The linearizability and time-invariance of the framework enable us to perform eigen decomposition, which is a powerful tool for root-cause analysis of SSO modes and the design of damping controllers. In addition, the DP modeling approach facilitates faster simulation of large-scale systems. The generalized framework is validated with EMTDC/PSCAD simulations using the IEEE first benchmark model for subsynchronous resonance and the modified IEEE 4-machine system. Several use cases are presented on the modified IEEE 68-bus system with two GFL IBRs to show the applicability of the framework. First, time- and frequency-domain analyses of the IBR-induced SSO mode are presented. Then, two solutions are proposed to damp the poorly damped SSO mode: (a) a decentralized controller is designed using particle swarm optimization, and (b) the control of one GFL IBR is replaced by GFM control. Finally, the impact of AI DC load on primary frequency response of the system and the multi-mass turbines of the SGs are studied.

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arXiv2026

A Dynamic Phasor Framework for Analysis of IBR-Induced SSOs in Multi-Machine Systems

We propose a generalized dynamic phasor (DP) framework to analyze inverter-based resources (IBRs) connected to multi-machine systems under balanced and unbalanced conditions. It captures subsynchronous oscillations (SSOs) induced by grid-following (GFL) IBRs. The linearizability and time invariance of the framework enables us to perform eigen decomposition, which is a powerful tool for root-cause analysis of the SSO modes and damping controller design. The same framework also enables analysis of excitation of the SSO modes in presence of data center (DC) loads. The GFL IBRs are modeled in their respective $dq$-frame DPs and the detailed model of synchronous generators (SGs) along with dynamic transmission network models are represented in $pnz$-frame DPs. Several case studies are performed on the modified IEEE two-area benchmark system, where $2$ SGs are replaced by GFL IBRs and validated with EMTDC/PSCAD simulations. First, time- and frequency-domain analyses of the SSO mode are presented followed by the design of a robust decentralized $\mathcal{H}_\infty$ damping controller based on local signals of the GFL IBRs. Second, the dynamic behavior of the system following an unbalanced fault is demonstrated that is damped by the proposed damping controller. Finally, excitation of the SSO mode in presence of DC load is exhibited and its locational impact is analytically quantified.

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arXiv2026

Willems' Fundamental Lemma with Large Noisy Fragmented Dataset

Willems' Fundamental Lemma enables parameterizing all trajectories generated by a Linear Time-Invariant (LTI) system directly from data. However, this lemma relies on the assumption of noiseless measurements. In this paper, we provide an approach that enables the applicability of Willems' Fundamental Lemma with a large noisy-input, noisy-output fragmented dataset, without requiring prior knowledge of the noise distribution. We introduce a computationally tractable and lightweight algorithm that, despite processing a large dataset, executes in the order of seconds to estimate the invariants of the underlying system, which is obscured by noise. The simulation results demonstrate the effectiveness of the proposed method.

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arXiv2026

Robust Data-Driven Invariant Sets for Nonlinear Systems

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute robust polytopic contractive sets for unknown nonlinear systems operating under persistent bounded process noise and state-input constraints. Rather than attempting to identify a single, potentially nominal model, we utilize a finite data set to construct a polytopic consistency set--a rigorous geometric boundary encapsulating all possible system dynamics compatible with the noisy measurements. The core contribution of this work extends an established sufficient condition for λ contractiveness into the data-driven setting. Crucially, we prove that enforcing this condition strictly over the vertices of the consistency set guarantees robust invariance.

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arXiv2025

A reference frame-based microgrid primary control for ensuring global convergence to a periodic orbit

Power systems with a high penetration of renewable generation are vulnerable to frequency oscillation and voltage instability. Traditionally, the stability of power systems is considered either in terms of local stability or as an angle oscillator synchronization problem with the simplifying assumption that the dynamics of the amplitudes are on much shorter time scales. Without this assumption, however, the steady state being studied is essentially a limit cycle with the convergence of its orbit in question. In this paper, we present a method to analyze the orbital stability of a microgrid and propose a voltage controller for the inverter-interfaced renewable generators. The main hurdle to the problem lies in the constant terms in the rotating internal reference frames of each generator. We extend the shifted passivity of port-Hamiltonian systems to the analysis of limit cycles and prove that, if the system is shifted passive without considering these constant terms, then the periodic orbit is globally attractive. To the best of our knowledge, this is the first global stability result for non-nominal steady states of the microgrid in the full state space, which provides new insights into the synchronization phenomenon where the dissipativity of the system ensures convergence. The proposed controller is verified with a test microgrid, demonstrating its stability and transient smoothness compared to the standard droop control.

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arXiv2025

Power System Electromagnetic Transient Stability: an Analysis Based on Convergent Hamiltonian

Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance representations. However, this simplification is inadequate for the growing penetration of fast-switching power electronic devices. Attempts to extend the existing theories to include electromagnetic dynamics lead to overly conservative stability conditions. To tackle this problem more directly, we study the condition under which the power source and dissipation in the electromagnetic dynamics tend to balance each other asymptotically. This is equivalent to the convergence of the Hamiltonian (total stored energy) and can be shown to imply transient stability. Using contraction analysis, we prove that this property holds for a large class of time-varying port-Hamiltonian systems with (i) constant damping matrix and (ii) strictly convex Hamiltonian. Then through port-Hamiltonian modeling of the electromagnetic dynamics, we obtain that the synchronized steady state of the power system is globally stable if it exists. This result provides new insights into the reliable operation of power systems. The proposed theory is illustrated in the simulation results of a two-machine system.

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arXiv2023

Parsimonious System Identification from Fragmented Quantized Measurements

Quantization is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system identification no longer applicable. In this work, we propose a method for parsimonious linear time invariant system identification when only quantized observations, discerned from noisy data, are available. More formally, given a priori information on the system, represented by a compact set containing the poles of the system, and quantized realizations, our algorithm aims at identifying the least order system that is compatible with the available information. The proposed approach takes also into account that the available data can be subject to fragmentation. Our proposed algorithm relies on an ADMM approach to solve a $\ell_{p},(0<p<1),$ quasi-norm objective problem. Numerical results highlight the performance of the proposed approach when compared to the $\ell_{1}$ minimization in terms of the sparsity of the induced solution.

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arXiv2023

Lp Quasi-norm Minimization: Algorithm and Applications

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This paper proposes a heuristic method for retrieving sparse approximate solutions of optimization problems via minimizing the $\ell_{p}$ quasi-norm, where $0<p<1$. An iterative two-block ADMM algorithm for minimizing the $\ell_{p}$ quasi-norm subject to convex constraints is proposed. For $p=s/q<1$, $s,q \in \mathbb{Z}_{+}$, the proposed algorithm requires solving for the roots of a scalar degree $2q$ polynomial as opposed to applying a soft thresholding operator in the case of $\ell_{1}$. The merit of that algorithm relies on its ability to solve the $\ell_{p}$ quasi-norm minimization subject to any convex set of constraints. However, it suffers from low speed, due to a convex projection step in each iteration, and the lack of mathematical convergence guarantee. We then aim to vanquish these shortcomings by relaxing the assumption on the constraints set to be the set formed due to convex and differentiable, with Lipschitz continuous gradient, functions, i.e. specifically, polytope sets. Using a proximal gradient step, we mitigate the convex projection step and hence enhance the algorithm speed while proving its convergence. We then present various applications where the proposed algorithm excels, namely, matrix rank minimization, sparse signal reconstruction from noisy measurements, sparse binary classification, and system identification. The results demonstrate the significant gains obtained by the proposed algorithm compared to those via $\ell_{1}$ minimization.

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arXiv2021

Model Predictive Control approach to adaptive messaging intervention for physical activity

In this work, we have developed a framework for synthesizing data driven controllers for a class of uncertain switched systems arising in an application to physical activity interventions. In particular, we present an application of probabilistic model predictive control to design an efficient, tractable, and adaptive intervention using behavioral data sets i.e. physical activity behavior. The models of physical activity for each individual are provided for the design of controllers that maximize the probability of achieving a desired physical activity goal subject to intervention specifications. We have tailored the mixed-integer programming-based approach for evaluating the Model Predictive Control decision at each time step.

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arXiv2019

Comparison of Different Spike Sorting Subtechniques Based on Rat Brain Basolateral Amygdala Neuronal Activity

Developing electrophysiological recordings of brain neuronal activity and their analysis provide a basis for exploring the structure of brain function and nervous system investigation. The recorded signals are typically a combination of spikes and noise. High amounts of background noise and possibility of electric signaling recording from several neurons adjacent to the recording site have led scientists to develop neuronal signal processing tools such as spike sorting to facilitate brain data analysis. Spike sorting plays a pivotal role in understanding the electrophysiological activity of neuronal networks. This process prepares recorded data for interpretations of neurons interactions and understanding the overall structure of brain functions. Spike sorting consists of three steps: spike detection, feature extraction, and spike clustering. There are several methods to implement each of spike sorting steps. This paper provides a systematic comparison of various spike sorting sub-techniques applied to real extracellularly recorded data from a rat brain basolateral amygdala. An efficient sorted data resulted from careful choice of spike sorting sub-methods leads to better interpretation of the brain structures connectivity under different conditions, which is a very sensitive concept in diagnosis and treatment of neurological disorders. Here, spike detection is performed by appropriate choice of threshold level via three different approaches. Feature extraction is done through PCA and Kernel PCA methods, which Kernel PCA outperforms. We have applied four different algorithms for spike clustering including K-means, Fuzzy C-means, Bayesian and Fuzzy maximum likelihood estimation. As one requirement of most clustering algorithms, optimal number of clusters is achieved through validity indices for each method. Finally, the sorting results are evaluated using inter-spike interval histograms.

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arXiv2019

Identification of Switched Autoregressive and Switched Autoregressive Exogenous Systems from Large Noisy Data Sets

The paper introduces novel methodologies for the identification of coefficients of switched autoregressive and switched autoregressive exogenous linear models. We consider cases which system's outputs are contaminated by possibly large values of noise for the both case of measurement noise in switched autoregressive models and process noise in switched autoregressive exogenous models. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise, which are compatible with the collected data. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.

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arXiv2019

Identification of Switched Autoregressive Systems from Large Noisy Data Sets

The paper introduces a novel methodology for the identification of coefficients of switched autoregressive linear models. We consider the case when the system's outputs are contaminated by possibly large values of measurement noise. It is assumed that only partial information on the probability distribution of the noise is available. Given input-output data, we aim at identifying switched system coefficients and parameters of the distribution of the noise which are compatible with the collected data. System dynamics are estimated through expected values computation and by exploiting the strong law of large numbers. We demonstrate the efficiency of the proposed approach with several academic examples. The method is shown to be extremely effective in the situations where a large number of measurements is available; cases in which previous approaches based on polynomial or mixed-integer optimization cannot be applied due to very large computational burden.

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arXiv2019

Identification of Markov Jump Autoregressive Processes from Large Noisy Data Sets

This paper introduces a novel methodology for the identification of switching dynamics for switched autoregressive linear models. Switching behavior is assumed to follow a Markov model. The system's outputs are contaminated by possibly large values of measurement noise. Although the procedure provided can handle other noise distributions, for simplicity, it is assumed that the distribution is Normal with unknown variance. Given noisy input-output data, we aim at identifying switched system coefficients, parameters of the noise distribution, dynamics of switching and probability transition matrix of Markovian model. System dynamics are estimated using previous results which exploit algebraic constraints that system trajectories have to satisfy. Switching dynamics are computed with solving a maximum likelihood estimation problem. The efficiency of proposed approach is shown with several academic examples. Although the noise to output ratio can be high, the method is shown to be extremely effective in the situations where a large number of measurements is available.

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arXiv2018

Randomized opinion dynamics over networks: influence estimation from partial observations

In this paper, we propose a technique for the estimation of the influence matrix in a sparse social network, in which $n$ individual communicate in a gossip way. At each step, a random subset of the social actors is active and interacts with randomly chosen neighbors. The opinions evolve according to a Friedkin and Johnsen mechanism, in which the individuals updates their belief to a convex combination of their current belief, the belief of the agents they interact with, and their initial belief, or prejudice. Leveraging recent results of estimation of vector autoregressive processes, we reconstruct the social network topology and the strength of the interconnections starting from \textit{partial observations} of the interactions, thus removing one of the main drawbacks of finite horizon techniques. The effectiveness of the proposed method is shown on randomly generation networks.

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arXiv2018

Parsimonious Volterra System Identification

In this short paper, we aim at developing algorithms for sparse Volterra system identification when the system to be identified has infinite impulse response. Assuming that the impulse response is represented as a sum of exponentials and given input-output data, the problem of interest is to find the "simplest" nonlinear Volterra model which is compatible with the a priori information and the collected data. By simplest, we mean the model whose impulse response has the least number of exponentials. The algorithms provided are able to handle both fragmented data and measurement noise. Academic examples at the end of paper show the efficacy of proposed approach.

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