arXiv subjects

Rodrigo A. González

Publications and source records attributed to Rodrigo A. González.

At least 19 recordsLinked to original sources

arXiv2026

The Zonotopic Mixture Filter

State estimation is commonly posed in either a probabilistic or an unknown-but-bounded framework. The former requires a fully specified noise distribution, typically with unbounded support, while the latter yields guaranteed enclosures that carry no probabilistic weighting. Bridging these noise descriptions, this paper proposes a zonotopic mixture noise model, in which the noise is generated by drawing a zonotope from a finite collection according to fixed probabilities and then realizing an arbitrary element of it. For this noise model, we derive the zonotopic mixture filter, which propagates a bank of zonotopic Kalman filters over mode histories, discards the histories falsified by the data, and weights the surviving ones by their relative probability. The resulting state enclosures yield guaranteed coverage probabilities and remain valid for every noise realization compatible with the bounds, and a greedy mixture reduction scheme preserves these statistical guarantees while keeping the representation tractable. Numerical examples illustrate the proposed approach and its potential benefits over related state estimation methods.

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arXiv2026

D-Optimized Sampling Design for System Identification

Traditional system identification with multisine inputs relies on uniform sampling and periodic excitation to preserve Fourier orthogonality and avoid spectral leakage, limiting its use in scenarios with irregular sampling or nonperiodic inputs. This work investigates continuous-time system identification under nonperiodic multisine excitation and nonuniform sampling. We develop a nonparametric frequency response function estimator suited to such conditions and design irregular sampling schemes that enhance the informativeness of measurements and reduce spectral leakage. The proposed sampling scheme improve the statistical accuracy of system identification in settings where periodic excitation is impractical.

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arXiv2026

End-to-End ILC for Repetitive Untrackable Tasks: A Cooperative Game Perspective

An inherent assumption of perfect tracking in iterative learning control (ILC) is that there exists an ILC input such that the generated output can track the desired trajectory reference. This assumption may fail in practice, which gives rise to desired but untrackable tasks. This paper gives an end-to-end ILC design for repetitive untrackable tasks in closed-loop systems. The reference input is trial-to-trial updated together with the ILC feedforward input based on the measurement data. This two-player behavior of the closed-loop ILC system is investigated from a cooperative game perspective. A sufficient condition for the two-player end-to-end ILC to have a lower cost than the one-player norm optimal ILC (NOILC) is discovered. Finally, a numerical example is given to verify the effectiveness of the developed method.

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arXiv2026

Structured identification of multivariable modal systems

Physically interpretable models are essential for next-generation industrial systems, as these representations enable effective control, support design validation, and provide a foundation for monitoring strategies. The aim of this paper is to develop a system identification framework for estimating modal models of complex multivariable mechanical systems from frequency response data. To achieve this, a two-step structured identification algorithm is presented, where an additive model is first estimated using a refined instrumental variable method and subsequently projected onto a modal form. The developed identification method provides accurate, physically-relevant, minimal-order models, for both generally-damped and proportionally damped modal systems. The effectiveness of the proposed method is demonstrated through experimental validation on a prototype wafer-stage system, which features a large number of spatially distributed actuators and sensors and exhibits complex flexible dynamics.

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arXiv2025

Sample-Efficient Counterfactual Tuning for Compressor Pressure Control

In controlled industrial environments, ensuring safety and performance during controller tuning is a challenging and critical task. In particular, control loops in compressor-plenum-throttle systems cannot tolerate costly interruptions, and aggressive excitation may lead to unsafe operating regimes. Given the wide availability of historical data, this paper introduces a counterfactual explainability approach for sample-efficient retuning of compressor control loops. The proposed data-driven algorithm determines, without an explicit plant model or previous control law, the smallest controller adjustment required to achieve predefined performance specifications while guaranteeing stability. The effectiveness of the method is demonstrated through an extensive Monte Carlo simulation study.

math.OC↗

arXiv2025

Finite Sample MIMO System Identification with Multisine Excitation: Nonparametric, Direct, and Two-step Parametric Estimators

Multisine excitations are widely used for identifying multi-input multi-output systems due to their periodicity, data compression properties, and control over the input spectrum. Despite their popularity, the finite sample statistical properties of frequency-domain estimators under multisine excitation, for both nonparametric and parametric settings, remain insufficiently understood. This paper develops a finite-sample statistical framework for least-squares estimation of the frequency response function (FRF) and its implications for parametric modeling. First, we derive exact distributional and covariance properties of the FRF estimator, explicitly accounting for aliasing effects under slow sampling regimes, and establish conditions for unbiasedness, uncorrelatedness, and consistency across multiple experiments. Second, we show that the FRF estimate is a sufficient statistic for any parametric model under Gaussian noise, leading to an exact equivalence between optimal two stage frequency-domain methods and time-domain prediction error and maximum likelihood estimation. This equivalence is shown to yield finite-sample concentration bounds for parametric maximum likelihood estimators, enabling rigorous uncertainty quantification, and closed-form prediction error method estimators without iterative optimization. The theoretical results are demonstrated in a representative case study.

stat.ME↗

arXiv2025

Filtering in Multivariate Systems with Quantized Measurements using a Gaussian Mixture-Based Indicator Approximation

This work addresses the problem of state estimation in multivariable dynamic systems with quantized outputs, a common scenario in applications involving low-resolution sensors or communication constraints. A novel method is proposed to explicitly construct the probability mass function associated with the quantized measurements by approximating the indicator function of each region defined by the quantizer using Gaussian mixture models. Unlike previous approaches, this technique generalizes to any number of quantized outputs without requiring case-specific numerical solutions, making it a scalable and efficient solution. Simulation results demonstrate that the proposed filter achieves high accuracy in state estimation, both in terms of fidelity of the filtering distributions and mean squared error, while maintaining significantly reduced computational cost.

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arXiv2025

Truncated Gaussian Noise Estimation in State-Space Models

Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space system identification, the prevalent practice entails constructing models under Gaussian noise assumptions, which can lead to inaccuracies when the noise follows bounded distributions. With the aim of generalizing the Gaussian noise assumption to potentially truncated densities, this paper introduces a method for estimating the noise parameters in a state-space model subject to truncated Gaussian noise. Our proposed data-driven approach is rooted in maximum likelihood principles combined with the Expectation-Maximization algorithm. The efficacy of the proposed approach is supported by a simulation example.

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arXiv2025

Simultaneous Input and State Estimation under Output Quantization: A Gaussian Mixture approach

Simultaneous Input and State Estimation (SISE) enables the reconstruction of unknown inputs and internal states in dynamical systems, with applications in fault detection, robotics, and control. While various methods exist for linear systems, extensions to systems with output quantization are scarce, and no formal connections to limit Kalman filters are known in this context. This work addresses these gaps by proposing a novel SISE algorithm for linear systems with quantized output measurements. The proposed algorithm introduces a Gaussian mixture model formulation of the observation model, which leads to closed-form recursive equations in the form of a Gaussian sum filter. In the absence of input prior knowledge, the recursions are shown to converge to a limit-case SISE algorithm, implementable as a bank of linear SISE filters running in parallel. A simulation example is presented to illustrate the effectiveness of the proposed approach.

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arXiv2025

Statistically Optimal Structured Additive MIMO Continuous-time System Identification

Many applications in mechanical, acoustic, and electronic engineering require estimating complex dynamical models, often represented as additive multi-input multi-output (MIMO) transfer functions with structural constraints. This paper introduces a two-stage procedure for estimating structured additive MIMO models, where structural constraints are enforced through a weighted nonlinear least-squares projection of the parameter vector initially estimated using a recently developed refined instrumental variables algorithm. The proposed approach is shown to be consistent and asymptotically efficient in open-loop scenarios. In closed-loop settings, it remains consistent despite potential noise model misspecification and achieves minimum covariance among all instrumental variable estimators. Extensive simulations are performed to validate the theoretical findings, and to show the efficacy of the proposed approach.

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arXiv2025

The Quadrature Gaussian Sum Filter and Smoother for Wiener Systems

Block-Oriented Nonlinear (BONL) models, particularly Wiener models, are widely used for their computational efficiency and practicality in modeling nonlinear behaviors in physical systems. Filtering and smoothing methods for Wiener systems, such as particle filters and Kalman-based techniques, often struggle with computational feasibility or accuracy. This work addresses these challenges by introducing a novel Gaussian Sum Filter for Wiener system state estimation that is built on a Gauss-Legendre quadrature approximation of the likelihood function associated with the output signal. In addition to filtering, a two-filter smoothing strategy is proposed, enabling accurate computation of smoothed state distributions at single and consecutive time instants. Numerical examples demonstrate the superiority of the proposed method in balancing accuracy and computational efficiency compared to traditional approaches, highlighting its benefits in control, state estimation and system identification, for Wiener systems.

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arXiv2025

Recursive Identification of Structured Systems: An Instrumental-Variable Approach Applied to Mechanical Systems

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers limited physical interpretability. The objective of this paper is to develop a real-time parameter estimation algorithm aimed at identifying time-varying dynamics within an interpretable model structure. An additive model structure is adopted for this purpose, which offers enhanced parsimony and is shown to be particularly suitable for mechanical systems. The proposed approach integrates the recursive simplified refined instrumental variable method with block-coordinate descent to minimize an exponentially-weighted output error cost function. This novel recursive identification method delivers parametric continuous-time additive models and is applicable in both open-loop and closed-loop controlled systems. Its efficacy is shown using numerical simulations and is further validated using experimental data to detect the time-varying resonance dynamics of a flexible beam system. These results demonstrate the effectiveness of the proposed approach for online and interpretable estimation for advanced monitoring and control applications.

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arXiv2024

Sampling in Parametric and Nonparametric System Identification: Aliasing, Input Conditions, and Consistency

The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for perfect signal reconstructability, careful consideration is required when identifying parametric and nonparametric models. In this letter, a comprehensive statistical analysis of estimators under slow sampling is performed. Necessary and sufficient conditions are obtained for unbiased estimates of the frequency response function beyond the Nyquist frequency, and it is shown that consistency of parametric estimators can be achieved even if input frequencies overlap after aliasing. Monte Carlo simulations confirm the theoretical properties.

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arXiv2024

Identification of Additive Continuous-time Systems in Open and Closed loop

When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system. Traditional linear system identification may not consider the most parsimonious model when relying solely on unfactored transfer functions, which typically result from standard direct approaches. This paper presents a novel identification method that delivers additive models for both open and closed-loop setups. The estimators that are derived are shown to be generically consistent, and can admit the identification of marginally stable additive systems. Numerical simulations show the efficacy of the proposed approach, and its performance in identifying a modal representation of a flexible beam is verified using experimental data.

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arXiv2024

Grey-box Recursive Parameter Identification of a Nonlinear Dynamic Model for Mineral Flotation

This study presents a grey-box recursive identification technique to estimate key parameters in a mineral flotation process across two scenarios. The method is applied to a nonlinear physics-based dynamic model validated at a laboratory scale, allowing real-time updates of two model parameters, n and C, in response to changing conditions. The proposed approach effectively adapts to process variability and allows for continuous adjustments based on operational fluctuations, resulting in a significantly improved estimation of concentrate grade - one key performance indicator. In Scenario 1, parameters n and C achieved fit metrics of 97.99 and 96.86, respectively, with concentrate grade estimations improving from 75.1 to 98.69 using recursive identification. In Scenario 2, the fit metrics for n and C were 96.27 and 95.48, respectively, with the concentrate grade estimations increasing from 96.27 to 99.45 with recursive identification. The results demonstrate the effectiveness of the proposed grey-box recursive identification method in accurately estimating parameters and predicting concentrate grade in a mineral flotation process.

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arXiv2024

Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop

Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results.

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arXiv2024

Statistical Analysis of Block Coordinate Descent Algorithms for Linear Continuous-time System Identification

Block coordinate descent is an optimization technique that is used for estimating multi-input single-output (MISO) continuous-time models, as well as single-input single output (SISO) models in additive form. Despite its widespread use in various optimization contexts, the statistical properties of block coordinate descent in continuous-time system identification have not been covered in the literature. The aim of this paper is to formally analyze the bias properties of the block coordinate descent approach for the identification of MISO and additive SISO systems. We characterize the asymptotic bias at each iteration, and provide sufficient conditions for the consistency of the estimator for each identification setting. The theoretical results are supported by simulation examples.

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arXiv2024

Kernel-based identification using Lebesgue-sampled data

Sampling in control applications is increasingly done non-equidistantly in time. This includes applications in motion control, networked control, resource-aware control, and event-based control. Some of these applications, like the ones where displacement is tracked using incremental encoders, are driven by signals that are only measured when their values cross fixed thresholds in the amplitude domain. This paper introduces a non-parametric estimator of the impulse response and transfer function of continuous-time systems based on such amplitude-equidistant sampling strategy, known as Lebesgue sampling. To this end, kernel methods are developed to formulate an algorithm that adequately takes into account the bounded output uncertainty between the event timestamps, which ultimately leads to more accurate models and more efficient output sampling compared to the equidistantly-sampled kernel-based approach. The efficacy of our proposed method is demonstrated through a mass-spring damper example with encoder measurements and extensive Monte Carlo simulation studies on system benchmarks.

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