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Cristian R. Rojas

Publications and source records attributed to Cristian R. Rojas.

At least 37 records · Page 2Linked to original sources
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

Balancing Application Relevant and Sparsity Revealing Excitation in Input Design

The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is no constraint on the mutual coherence, making it difficult to handle sparse estimation. This paper aims to tackle this issue for fixed denominator models, which include Laguerre, Kautz, and generalized orthonormal basis function expansion models, for example. The paper proposes an optimal input design method where the achieved Fisher information matrix is fitted to the desired Fisher matrix, together with a coordinate transformation designed to make the regressors in the transformed coordinates have low mutual coherence. The method can be used together with any sparse estimation method and any desired Fisher matrix. A numerical study shows its potential for alleviating the problem of model order selection when used in conjunction with, for example, classical methods such as the Akaike Information Criterion.

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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

Weighted Least-Squares PARSIM

Subspace identification methods (SIMs) have proven very powerful for estimating linear state-space models. To overcome the deficiencies of classical SIMs, a significant number of algorithms has appeared over the last two decades, where most of them involve a common intermediate step, that is to estimate the range space of the extended observability matrix. In this contribution, an optimized version of the parallel and parsimonious SIM (PARSIM), PARSIM\textsubscript{opt}, is proposed by using weighted least-squares. It not only inherits all the benefits of PARSIM but also attains the best linear unbiased estimator for the above intermediate step. Furthermore, inspired by SIMs based on the predictor form, consistent estimates of the optimal weighting matrix for weighted least-squares are derived. Essential similarities, differences and simulated comparisons of some key SIMs related to our method are also presented.

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arXiv2024

A Weighted Least-Squares Method for Non-Asymptotic Identification of Markov Parameters from Multiple Trajectories

Markov parameters play a key role in system identification. There exists many algorithms where these parameters are estimated using least-squares in a first, pre-processing, step, including subspace identification and multi-step least-squares algorithms, such as Weighted Null-Space Fitting. Recently, there has been an increasing interest in non-asymptotic analysis of estimation algorithms. In this contribution we identify the Markov parameters using weighted least-squares and present non-asymptotic analysis for such estimator. To cover both stable and unstable systems, multiple trajectories are collected. We show that with the optimal weighting matrix, weighted least-squares gives a tighter error bound than ordinary least-squares for the case of non-uniformly distributed measurement errors. Moreover, as the optimal weighting matrix depends on the system's true parameters, we introduce two methods to consistently estimate the optimal weighting matrix, where the convergence rate of these estimates is also provided. Numerical experiments demonstrate improvements of weighted least-squares over ordinary least-squares in finite sample settings.

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arXiv2024

Finite Sample Analysis for a Class of Subspace Identification Methods

While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical analysis of SIMs remains an open problem, especially in the non-asymptotic regime. In this work, we provide a finite sample analysis for a class of SIMs, which reveals that the convergence rates for estimating Markov parameters and system matrices are $\mathcal{O}(1/\sqrt{N})$, in line with classical asymptotic results. Based on the observation that the model format in classical SIMs becomes non-causal because of a projection step, we choose a parsimonious SIM that bypasses the projection step and strictly enforces a causal model to facilitate the analysis, where a bank of ARX models are estimated in parallel. Leveraging recent results from finite sample analysis of an individual ARX model, we obtain an overall error bound of an array of ARX models and proceed to derive error bounds for system matrices via robustness results for the singular value decomposition.

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arXiv2024

Kernel-based learning with guarantees for multi-agent applications

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori knowledge about the phenomenon under investigation and delivers a model with corresponding non-asymptotic high probability error bounds. Both non-asymptotic analysis of the method and numerical simulation results are presented and discussed in the paper.

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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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arXiv2023

Unraveling the Control Engineer's Craft with Neural Networks

Many industrial processes require suitable controllers to meet their performance requirements. More often, a sophisticated digital twin is available, which is a highly complex model that is a virtual representation of a given physical process, whose parameters may not be properly tuned to capture the variations in the physical process. In this paper, we present a sim2real, direct data-driven controller tuning approach, where the digital twin is used to generate input-output data and suitable controllers for several perturbations in its parameters. State-of-the art neural-network architectures are then used to learn the controller tuning rule that maps input-output data onto the controller parameters, based on artificially generated data from perturbed versions of the digital twin. In this way, as far as we are aware, we tackle for the first time the problem of re-calibrating the controller by meta-learning the tuning rule directly from data, thus practically replacing the control engineer with a machine learning model. The benefits of this methodology are illustrated via numerical simulations for several choices of neural-network architectures.

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arXiv2023

Minimax Two-Stage Gradient Boosting for Parameter Estimation

Parameter estimation is an important sub-field in statistics and system identification. Various methods for parameter estimation have been proposed in the literature, among which the Two-Stage (TS) approach is particularly promising, due to its ease of implementation and reliable estimates. Among the different statistical frameworks used to derive TS estimators, the min-max framework is attractive due to its mild dependence on prior knowledge about the parameters to be estimated. However, the existing implementation of the minimax TS approach has currently limited applicability, due to its heavy computational load. In this paper, we overcome this difficulty by using a gradient boosting machine (GBM) in the second stage of TS approach. We call the resulting algorithm the Two-Stage Gradient Boosting Machine (TSGBM) estimator. Finally, we test our proposed TSGBM estimator on several numerical examples including models of dynamical systems.

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arXiv2023

DRCFS: Doubly Robust Causal Feature Selection

Knowing the features of a complex system that are highly relevant to a particular target variable is of fundamental interest in many areas of science. Existing approaches are often limited to linear settings, sometimes lack guarantees, and in most cases, do not scale to the problem at hand, in particular to images. We propose DRCFS, a doubly robust feature selection method for identifying the causal features even in nonlinear and high dimensional settings. We provide theoretical guarantees, illustrate necessary conditions for our assumptions, and perform extensive experiments across a wide range of simulated and semi-synthetic datasets. DRCFS significantly outperforms existing state-of-the-art methods, selecting robust features even in challenging highly non-linear and high-dimensional problems.

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arXiv2023

On the Relation between Discrete and Continuous-time Refined Instrumental Variable Methods

The Refined Instrumental Variable method for discrete-time systems (RIV) and its variant for continuous-time systems (RIVC) are popular methods for the identification of linear systems in open-loop. The continuous-time equivalent of the transfer function estimate given by the RIV method is commonly used as an initialization point for the RIVC estimator. In this paper, we prove that these estimators share the same converging points for finite sample size when the continuous-time model has relative degree zero or one. This relation does not hold for higher relative degrees. Then, we propose a modification of the RIV method whose continuous-time equivalent is equal to the RIVC estimator for any non-negative relative degree. The implications of the theoretical results are illustrated via a simulation example.

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arXiv2023

Decentralized diffusion-based learning under non-parametric limited prior knowledge

We study the problem of diffusion-based network learning of a nonlinear phenomenon, $m$, from local agents' measurements collected in a noisy environment. For a decentralized network and information spreading merely between directly neighboring nodes, we propose a non-parametric learning algorithm, that avoids raw data exchange and requires only mild \textit{a priori} knowledge about $m$. Non-asymptotic estimation error bounds are derived for the proposed method. Its potential applications are illustrated through simulation experiments.

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arXiv2023

Diagnosing and Augmenting Feature Representations in Correctional Inverse Reinforcement Learning

Robots have been increasingly better at doing tasks for humans by learning from their feedback, but still often suffer from model misalignment due to missing or incorrectly learned features. When the features the robot needs to learn to perform its task are missing or do not generalize well to new settings, the robot will not be able to learn the task the human wants and, even worse, may learn a completely different and undesired behavior. Prior work shows how the robot can detect when its representation is missing some feature and can, thus, ask the human to be taught about the new feature; however, these works do not differentiate between features that are completely missing and those that exist but do not generalize to new environments. In the latter case, the robot would detect misalignment and simply learn a new feature, leading to an arbitrarily growing feature representation that can, in turn, lead to spurious correlations and incorrect learning down the line. In this work, we propose separating the two sources of misalignment: we propose a framework for determining whether a feature the robot needs is incorrectly learned and does not generalize to new environment setups vs. is entirely missing from the robot's representation. Once we detect the source of error, we show how the human can initiate the realignment process for the model: if the feature is missing, we follow prior work for learning new features; however, if the feature exists but does not generalize, we use data augmentation to expand its training and, thus, complete the correction. We demonstrate the proposed approach in experiments with a simulated 7DoF robot manipulator and physical human corrections.

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arXiv2023

Parsimonious Identification of Continuous-Time Systems: A Block-Coordinate Descent Approach

The identification of electrical, mechanical, and biological systems using data can benefit greatly from prior knowledge extracted from physical modeling. Parametric continuous-time identification methods can naturally incorporate this knowledge, which leads to interpretable and parsimonious models. However, some applications lead to model structures that lack parsimonious descriptions using unfactored transfer functions, which are commonly used in standard direct approaches for continuous-time system identification. In this paper we characterize this parsimony problem, and develop a block-coordinate descent algorithm that delivers parsimonious models by sequentially estimating an additive decomposition of the transfer function of interest. Numerical simulations show the efficacy of the proposed approach.

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arXiv2023

An EM Algorithm for Lebesgue-sampled State-space Continuous-time System Identification

This paper concerns the identification of continuous-time systems in state-space form that are subject to Lebesgue sampling. Contrary to equidistant (Riemann) sampling, Lebesgue sampling consists of taking measurements of a continuous-time signal whenever it crosses fixed and regularly partitioned thresholds. The knowledge of the intersample behavior of the output data is exploited in this work to derive an expectation-maximization (EM) algorithm for parameter estimation of the state-space and noise covariance matrices. For this purpose, we use the incremental discrete-time equivalent of the system, which leads to EM iterations of the continuous-time state-space matrices that can be computed by standard filtering and smoothing procedures. The effectiveness of the identification method is tested via Monte Carlo simulations.

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