Identification Of Continuous-time Systems Research Articles

Continuous-time MISO fractional system identification using higher-order-statistics

Continuous-time MISO fractional system identification using higher-order-statistics

Identification of Continuous-Time Systems With Irregular Samplings by Invariant-Subspace Based Method

Identification of Continuous-Time Systems With Irregular Samplings by Invariant-Subspace Based Method

Machine Learning Classification of Event-Related Brain Potentials during a Visual Go/NoGo Task.

Machine learning (ML) methods are increasingly being applied to analyze biological signals. For example, ML methods have been successfully applied to the human electroencephalogram (EEG) to classify neural signals as pathological or non-pathological and to predict working memory performance in healthy and psychiatric patients. ML approaches can quickly process large volumes of data to reveal patterns that may be missed by humans. This study investigated the accuracy of ML methods at classifying the brain's electrical activity to cognitive events, i.e., event-related brain potentials (ERPs). ERPs are extracted from the ongoing EEG and represent electrical potentials in response to specific events. ERPs were evoked during a visual Go/NoGo task. The Go/NoGo task requires a button press on Go trials and response withholding on NoGo trials. NoGo trials elicit neural activity associated with inhibitory control processes. We compared the accuracy of six ML algorithms at classifying the ERPs associated with each trial type. The raw electrical signals were fed to all ML algorithms to build predictive models. The same raw data were then truncated in length and fitted to multiple dynamic state space models of order nx using a continuous-time subspace-based system identification algorithm. The 4nx numerator and denominator parameters of the transfer function of the state space model were then used as substitutes for the data. Dimensionality reduction simplifies classification, reduces noise, and may ultimately improve the predictive power of ML models. Our findings revealed that all ML methods correctly classified the electrical signal associated with each trial type with a high degree of accuracy, and accuracy remained high after parameterization was applied. We discuss the models and the usefulness of the parameterization.

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

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

Closed-Loop Continuous-Time Subspace Identification with Prior Information

This paper presents a closed-loop continuous-time subspace identification method using prior information. Based on a rational inner function, a generalized orthonormal basis can be constructed, and the transformed noises have ergodicity features. The continuous-time stochastic system is converted into a discrete-time stochastic system by using generalized orthogonal basis functions. As is known to all, incorporating prior information into identification strategies can increase the precision of the identified model. To enhance the precision of the identification method, prior information is integrated through the use of constrained least squares, and principal component analysis is adopted to achieve the reliable estimate of the system. Moreover, the identification of open-loop models is the primary intent of the continuous-time system identification approaches. For closed-loop systems, the open-loop subspace identification methods may produce biased results. Principal component analysis, which reliably estimates closed-loop systems, provides a solution to this problem. The restricted least-squares method with an equality constraint is used to incorporate prior information into the impulse response following the principal component analysis. The input–output algebraic equation yielded an optimal multi-step-ahead predictor, and the equality constraints describe the prior information. The effectiveness of the proposed method is provided by numerical simulations.

Continuous-time modeling of financial returns based on Limit Order Book data

The Limit Order Book (LOB) of a financial security contains the list of buy and sell orders placed by traders on a single or across many exchanges for a given stock. As such, the amount of information contained in the LOB is much richer than that contained in the time history of the mean price, so it can potentially be exploited to model and predict more accurately the future returns. As far as we are aware, this work offers - for the first time - a dynamical systems perspective on the latter modeling problem, leading to a two-fold contribution: (i) we will define a new regressor, called Base Imbalance, and we will show that its predictive potential is more significant than the ones usually employed in the literature; (ii) we will discuss that the most suitable way to derive a model of the LOB dynamics is via continuous-time system identification, due to the event-based nature of the phenomenon at hand. The effectiveness of the proposed modeling strategy to be used in trading policies will be illustrated by means of a benchmark experimental data.

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 inter-pretable 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.

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.

Global terrestrial temperature modeling by using fractional models

Modeling the global climate system through the temperature output is a very challenging task. Knowing the fractional operator long memory property to well model diffusion phenomena with very few parameters, it is proposed in this paper to use fractional models for climate change modeling. System identification is applied for continuous-time system identification of multiple-input single-output (MISO) fractional order models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. Finally, the estimation with fractional models is carried out on real input/output data and provide a very good goodness fit of the global earth temperature.

CRONE Toolbox for system identification and modeling using fractional differentiation models

New developments for continuous-time system identification with fractional order models are proposed in the CRONE toolbox (version 2.0). Fully compatible since Matlab® 2020a, it includes time-domain identification algorithms for estimating continuous-time models directly from sampled data. In this new version 2.0, the reliability has been improved thanks to a complete revision of the classes and their unitary tests. Thanks to this new programming, the options arguments of the proposed functions have been simplified and updated. In order to help a new user, a tutorial has been completely revised as the CRONE_demos command and to handle the new options. A Guided User Interface (GUI) is now proposed, as the CroneIdentification application so that a user, familiar with the SystemIdentification GUI, can easily handle the system identification methods for preprocessing data, defining a model structure and estimating as well the coefficients and the differentiation orders.

Identification of Continuous-Time Systems with Multiple Unknown Time Delays from Sampled Data

The purpose of this work is to identify a multiple-input single-output (MISO) continuous time (CT) system with various unknown time delays using sampled data. A novel technique for simultaneously estimating system parameters and various time delays may be developed using a gradient algorithm. Indeed, we propose a new formulation of the identification problem which permits defining the generalized vector containing the time delays and the dynamic parameters. The gradient optimization algorithm with exact derivatives of the objective function with respect to the adjustable parameters has been suggested as an alternative for solving this optimization problem. The identification method can be easily implemented by a filtering procedure to generate the input/output time derivatives. In this sense, the proposed method, which is based on a state variable filter, intrinsically allows data filtering and thus simplifies the use of the method in a practical case. An analysis is then presented which proves the convergence of the algorithm, and robustness issues are discussed as well. Finally, the suggested technique is evaluated on simulated instances to ensure its validity and performance.

Online continuous time system identification in the presence of impulsive terms

SummaryOnline parameters estimation algorithms are proposed for continuous time systems subject to structured perturbations. Using a distribution framework, a matrix pencil structure, whose polynomial order is characterized by the nature of the singularities describing the impulsive effects, is proposed for the modeling of perturbed systems with different disturbance types. Then, using an appropriate projection subspace, the rectangular pencils are reformulated as square generalized eigenvalue problems subject to linear constraints, from which unperturbed regression are derived. This approach allows for the implementation of recursive estimation schemes, free of penalty terms. An identifiability analysis is also conducted, and theoretical results are illustrated with experimental and simulated data.

Unbiased Identification of Fractional Order System with Unknown Time-Delay Using Bias Compensation Method

In the field of engineering, time-delay is a typical occurrence. In reality, the inner dynamics of many industrial processes are impacted by delay or after-effect events. This paper discusses the identification of continuous-time fractional order system with unknown time-delay using the bias compensated least squares algorithm. The basic concept is to remove the imposed bias by including a correction term into the least squares estimations. The suggested approach makes a significant contribution by the estimation, iteratively, of fractional order system coefficients as well as the orders and the time-delay using a nonlinear optimization algorithm. The main advantage of this method is to provide a simple and powerful algorithm with good accuracy. The suggest method performances are assessed through two numerical examples.

Refined instrumental variable methods for unstable continuous-time systems in closed-loop

In continuous-time system identification, refined instrumental variable methods are widely used in open and closed-loop settings. Although their robustness and performance are well documented for stable systems, these estimators are not reliable for estimating unstable continuous-time models. The main difficulty we encounter in modeling unstable systems with refined instrumental variables is that the filtered regressor and instrument vectors, as well as the filtered output, become severely ill-conditioned if the model is unstable during the iterative process. In this work, we propose a solution to this problem by including a tailor-made all-pass filter in the prefiltering step. This approach is used for obtaining an extension of the least-squares state-variable filter method, as well as extensions for the refined instrumental variable method for continuous-time systems (RIVC) and its simplified embodiment (SRIVC), that admit the identification of unstable systems and are shown to minimise the prediction error upon convergence and as the sample size goes to infinity. In addition, several implementations of these methods are proposed depending on the intersample behaviour of the input (zero and first-order hold, multisine and arbitrary). The particular case when the plant has integral action is explicitly considered in this work. In an indirect system identification setting, an extension of the closed-loop version of the SRIVC method is also proposed and discussed in detail. Monte Carlo simulations are used to assess the performance of our methods.

Long-memory recursive prediction error method for identification of continuous-time fractional models

This paper deals with recursive continuous-time system identification using fractional-order models. Long-memory recursive prediction error method is proposed for recursive estimation of all parameters of fractional-order models. When differentiation orders are assumed known, least squares and prediction error methods, being direct extensions to fractional-order models of the classic methods used for integer-order models, are compared to our new method, the long-memory recursive prediction error method. Given the long-memory property of fractional models, Monte Carlo simulations prove the efficiency of our proposed algorithm. Then, when the differentiation orders are unknown, two-stage algorithms are necessary for both parameter and differentiation-order estimation. The performances of the new proposed recursive algorithm are studied through Monte Carlo simulations. Finally, the proposed algorithm is validated on a biological example where heat transfers in lungs are modeled by using thermal two-port network formalism with fractional models.

Theoretical and practical aspects of the convergence of the SRIVC estimator for over-parameterized models

The Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) is one of the most popular direct methods for linear continuous-time system identification. Only recently, some optimal asymptotic properties of this method have been proven. Here we provide a comprehensive analysis of the convergence of the SRIVC method for over-parameterized models. The results we derive are used to discuss practical aspects of the method and to analyze the behavior of the normalized error variance norm, which is a central part in Young’s Information Criterion for model order selection. The theoretical findings are validated through simulation examples.

Rational Orthonormal Bases, State Transformations, and Dissipativity

We establish formulas relating the state of a continuous-time system with that of the transformed one in a Takenaka–Malmquist–Kautz orthogonal basis. We use such relation to give a simple proof that if the original system is dissipative, then the transformed one is also dissipative with the same storage function. We apply our results to continuous-time subspace system identification.

System identification of MISO fractional systems: Parameter and differentiation order estimation

This paper deals with continuous-time system identification of multiple-input single-output (MISO) fractional differentiation models. When differentiation orders are assumed to be known, coefficients are estimated using the simplified refined instrumental variable method for continuous-time fractional models extended to the MISO case. For unknown differentiation orders, a two-stage optimization algorithm is proposed with the developed instrumental variable for coefficient estimation and a gradient-based algorithm for differentiation order estimation. A new definition of structured-commensurability (or S-commensurability) is introduced to better cope with differentiation order estimation. Three variants of the algorithm are then proposed: (i) first, all differentiation orders are set as integer multiples of a global S-commensurate order, (ii) then, the differentiation orders are set as integer multiples of a local S-commensurate orders (one S-commensurate order for each subsystem), (iii) finally, all differentiation orders are estimated by releasing the S-commensurability constraint. The first variant has the smallest number of parameters and is used as a good initial hit for the second variant which in turn is used as a good initial hit for the third variant. Such a progressive increase of the number of parameters allows better performance of the optimization algorithm evaluated by Monte Carlo simulation analysis.

Measurement and modeling of a flexible manipulator for vibration control using five-segment S-curve motion

User designed manipulators are widely used in industry as a part of automation. The design of lighter robotic arms is required for less energy consumption. Joints, structural features, and payload affect the dynamic behavior of manipulators. Even if the arms have sufficient structural rigidity, joints, or payloads further increase their flexibility. These factors should be considered at the design stage. Flexibility causes vibrations, and these vibrations negatively affect robot repeatability and processing speed. Reducing the vibration levels of flexible manipulators is an attractive issue for engineers and researchers. Accurate estimation of the mathematical model of flexible manipulators increases the success of vibration control. In this paper, the modeling and experiments for vibration control of a single-axis flexible curved manipulator with payload are considered. The experimental system is introduced to collect vibration responses synchronously at the tip of the curved manipulator for angular velocity input. The mathematical model of the manipulator is estimated using the continuous-time system identification (CTSI) method with a black-box model based on the experimental input/output (I/O) signals. A five-segment S-curve motion input based on the modal parameters is designed to suppress residual vibrations. Vibration control is successfully performed for different deceleration times of the designed S-curve motion input. The results showed that the residual vibrations from experiments and predicted models matched well for different cases depending on payload, angular position, and motion time.

Recursive Subspace Identification of Continuous-Time Systems Using Generalized Poisson Moment Functionals

Recursive Subspace Identification of Continuous-Time Systems Using Generalized Poisson Moment Functionals