Showing papers on "System identification published in 2019"
TL;DR: This survey focuses on evolving fuzzy rule-based models and neuro-fuzzy networks for clustering, classification and regression and system identification in online, real-time environments where learning and model development should be performed incrementally.
231 citations
TL;DR: This paper proposes to determine the regularization parameter using the weighted generalized cross-validation method at every iteration of ill-conditioned SNLLS problems based on the variable projection method to produce a consistent demand of decreasing at successive iterations.
Abstract: Separable nonlinear least-squares (SNLLS) problems arise frequently in many research fields, such as system identification and machine learning. The variable projection (VP) method is a very powerful tool for solving such problems. In this paper, we consider the regularization of ill-conditioned SNLLS problems based on the VP method. Selecting an appropriate regularization parameter is difficult because of the nonlinear optimization procedure. We propose to determine the regularization parameter using the weighted generalized cross-validation method at every iteration. This makes the original objective function changing during the optimization procedure. To circumvent this problem, we use an inequation to produce a consistent demand of decreasing at successive iterations. The approximation of the Jacobian of the regularized problem is also discussed. The proposed regularized VP algorithm is tested by the parameter estimation problem of several statistical models. Numerical results demonstrate the effectiveness of the proposed algorithm.
144 citations
TL;DR: The main contribution is the introduction of a mathematically rigorous and computationally tractable framework for stabilizing model predictive control with online parameter estimation to improve performance and reduce conservatism.
140 citations
TL;DR: In this paper, the authors model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort.
135 citations
TL;DR: An optimized improved Elman neural network based on a new hybrid optimization algorithm is proposed for increasing their efficiency in the next designs of the proton exchange membrane fuel cell.
132 citations
10 Jul 2019
TL;DR: This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis to give non-asymptotic guarantees on both estimation and controller performance.
Abstract: We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of state and input constraints. This framework involves a novel method for synthesizing robust constraint-satisfying feedback controllers, leveraging newly developed tools from system level synthesis. We connect statistical results with cost sub-optimality bounds to give non-asymptotic guarantees on both estimation and controller performance.
131 citations
01 Dec 2019
TL;DR: In this article, the authors analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics, and provide non-asymptotic high-probability upper bounds for the system parameter estimation errors.
Abstract: In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalman filter gain, given a single trajectory of output measurements over a finite horizon of length N. Based on a subspace identification algorithm and a finite number of N output samples, we provide non-asymptotic high-probability upper bounds for the system parameter estimation errors. Our analysis uses recent results from random matrix theory, self-normalized martingales and SVD robustness, in order to show that with high probability the estimation errors decrease with a rate of $1/\sqrt N$ up to logarithmic terms. Our non-asymptotic bounds not only agree with classical asymptotic results, but are also valid even when the system is marginally stable.
112 citations
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TL;DR: In this article, the authors investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems, and reveal that persistency of excitation is not necessary.
Abstract: The use of persistently exciting data has recently been popularized in the context of data-driven analysis and control. Such data have been used to assess system theoretic properties and to construct control laws, without using a system model. Persistency of excitation is a strong condition that also allows unique identification of the underlying dynamical system from the data within a given model class. In this paper, we develop a new framework in order to work with data that are not necessarily persistently exciting. Within this framework, we investigate necessary and sufficient conditions on the informativity of data for several data-driven analysis and control problems. For certain analysis and design problems, our results reveal that persistency of excitation is not necessary. In fact, in these cases data-driven analysis/control is possible while the combination of (unique) system identification and model-based control is not. For certain other control problems, our results justify the use of persistently exciting data as data-driven control is possible only with data that are informative for system identification.
105 citations
TL;DR: This paper describes a discrete-time dynamic system to model spin dynamics, and derives an estimation-theoretic bound, i.e., the Cramér-Rao bound, to characterize the signal-to-noise ratio (SNR) efficiency of an MR fingerprinting experiment.
Abstract: Magnetic resonance (MR) fingerprinting is a new quantitative imaging paradigm, which simultaneously acquires multiple MR tissue parameter maps in a single experiment. In this paper, we present an estimation-theoretic framework to perform experiment design for MR fingerprinting. Specifically, we describe a discrete-time dynamic system to model spin dynamics, and derive an estimation-theoretic bound, i.e., the Cramer-Rao bound, to characterize the signal-to-noise ratio (SNR) efficiency of an MR fingerprinting experiment. We then formulate an optimal experiment design problem, which determines a sequence of acquisition parameters to encode MR tissue parameters with the maximal SNR efficiency, while respecting the physical constraints and other constraints from the image decoding/reconstruction process. We evaluate the performance of the proposed approach with numerical simulations, phantom experiments, and in vivo experiments. We demonstrate that the optimized experiments substantially reduce data acquisition time and/or improve parameter estimation. For example, the optimized experiments achieve about a factor of two improvement in the accuracy of ${T}_{2}$ maps, while keeping similar or slightly better accuracy of ${T}_{1}$ maps. Finally, as a remarkable observation, we find that the sequence of optimized acquisition parameters appears to be highly structured rather than randomly/pseudo-randomly varying as is prescribed in the conventional MR fingerprinting experiments.
103 citations
TL;DR: This study presents a deep convolutional neural network (CNN)-based approach to estimate the dynamic response of a linear single-degree-of-freedom (SDOF) system, a nonlinear SDOF system, and an...
Abstract: This study presents a deep convolutional neural network (CNN)-based approach to estimate the dynamic response of a linear single-degree-of-freedom (SDOF) system, a nonlinear SDOF system, an...
102 citations
TL;DR: The focus is on meeting challenges that arise from system identification and damage assessment for the civil infrastructure but the presented theories also have a considerably broader applicability for inverse problems in science and technology.
Abstract: Bayesian inference provides a powerful approach to system identification and damage assessment for structures. The application of Bayesian method is motivated by the fact that inverse problems in s...
TL;DR: An online model identification method based on adaptive forgetting recursive total least squares (AF-RTLS) is proposed to compensate the noise effect and attenuate the identification bias of model parameters.
Abstract: Accurate estimation of power capacity is critical to ensure battery safety margins and optimize energy utilization. Power capacity estimators based on online identified equivalent circuit model have been widely investigated due to the high accuracy and affordable computing cost. However, the impact of noise corruption which is common in practice on such estimators has never been investigated. This paper scrutinizes the effect of noises on model identification, state of charge (SOC) and power capacity estimation. An online model identification method based on adaptive forgetting recursive total least squares (AF-RTLS) is proposed to compensate the noise effect and attenuate the identification bias of model parameters. A Luenberger observer is further used in combination with the AF-RTLS to estimate the SOC in real time. Leveraging the estimated model parameters and SOC, a multiconstraint analytical method is proposed to online estimate the power capacity. Simulation and experimental results verify that the proposed method is superior in terms of estimation accuracy and the robustness to noise corruption.
TL;DR: It is proved that ANN models are able to approximate every time-dependent model described by ODEs with any desired level of accuracy, and is tested on different problems, including the model reduction of two large-scale models.
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TL;DR: This work provides a data-dependent scheme for order selection and finds a realization of system parameters, corresponding to that order, by an approach that is closely related to the celebrated Kalman-Ho subspace algorithm, and shows that this realization is a good approximation of the underlying LTI system with high probability.
Abstract: We address the problem of learning the parameters of a stable linear time invariant (LTI) system with unknown latent space dimension, or \textit{order}, from its noisy input-output data. In particular, we focus on learning the parameters of the best lower order approximation allowed by the finite data. This is achieved by constructing a Hankel-like representation of the underlying system using ordinary least squares. Such a representation circumvents the non-convexities that typically arise in system identification, and it allows accurate estimation of the underlying LTI system. Our results rely on a careful analysis of a self-normalized martingale difference term that helps bound identification error up to logarithmic factors of the lower bound. We provide a data-dependent scheme for order selection and find a realization of system parameters, corresponding to that order, by an approach that is closely related to the celebrated Kalman-Ho subspace algorithm. We show that this realization is a good approximation of the underlying LTI system with high probability. Finally, we demonstrate that the proposed model order selection procedure is minimax optimal, i.e., for the given data length it is not always possible to estimate higher order models or find higher order approximations with reasonable accuracy.
TL;DR: The method is a parametric modeling technique based on sparse regularization capable of discovering the underlying governing equations of the system of interest from input-output data and successfully identifies the following structural systems from experimental data.
TL;DR: Numerical and experimental validation examples are used to demonstrate the effectiveness of the proposed UKF-UI algorithm for the simultaneous identification of nonlinear parameters and unknown external excitations using data fusion of partially measured system responses.
TL;DR: The results demonstrate the feasibility of an integrated strategy for analysing the theoretical possibility of determining the states, parameters and inputs to a system and solving the practical problem of actually estimating their values.
Abstract: In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.
TL;DR: In this article, a novel integral concurrent learning method is developed that removes the need to estimate state derivatives while maintaining parameter convergence properties, and a Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation.
Abstract: Concurrent learning is a recently developed adaptive update scheme that can be used to guarantee parameter convergence without requiring persistent excitation. However, this technique requires knowledge of state derivatives, which are usually not directly sensed and therefore must be estimated. A novel integral concurrent learning method is developed in this paper that removes the need to estimate state derivatives while maintaining parameter convergence properties. A Monte Carlo simulation illustrates improved robustness to noise compared to the traditional derivative formulation.
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TL;DR: This work describes this Koopman-based system identification method and its application to model predictive controller design, which yields an explicit control-oriented linear model rather than just a "black-box" input-output mapping.
Abstract: Controlling soft robots with precision is a challenge due in large part to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman Operator Theory offers a way to construct explicit linear dynamical models of soft robots and to control them using established model-based linear control methods. This method is data-driven, yet unlike other data-driven models such as neural networks, it yields an explicit control-oriented linear model rather than just a "black-box" input-output mapping. This work describes this Koopman-based system identification method and its application to model predictive controller design. A model and MPC controller of a pneumatic soft robot arm was constructed via the method, and its performance was evaluated over several trajectory following tasks in the real-world. On all of the tasks, the Koopman-based MPC controller outperformed a benchmark MPC controller based on a linear state-space model of the same system.
TL;DR: A practical and robust system identification modelling method for ship manoeuvring motion is presented, to alleviate the impact of noise-induced problems, such as parameter drift or over-fitting, on the model reliability.
Proceedings Article•
22 Jun 2019TL;DR: In this paper, a model and MPC controller of a pneumatic soft robot arm were constructed via the method, and its performance was evaluated over several trajectory following tasks in the real-world.
Abstract: Controlling soft robots with precision is a challenge due in large part to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman Operator Theory offers a way to construct explicit linear dynamical models of soft robots and to control them using established model-based linear control methods. This method is data-driven, yet unlike other data-driven models such as neural networks, it yields an explicit control-oriented linear model rather than just a "black-box" input-output mapping. This work describes this Koopman-based system identification method and its application to model predictive controller design. A model and MPC controller of a pneumatic soft robot arm was constructed via the method, and its performance was evaluated over several trajectory following tasks in the real-world. On all of the tasks, the Koopman-based MPC controller outperformed a benchmark MPC controller based on a linear state-space model of the same system.
TL;DR: This work improves the static framework that only works when measurements are from one single state, by further treating state changes in historical measurements as an unobserved latent variable, and incorporates the expectation-maximization (EM) algorithm to recover different hidden states in measurements.
Abstract: Grid topology and line parameters are essential for grid operation and planning, which may be missing or inaccurate in distribution grids. Existing data-driven approaches for recovering such information usually suffer from ignoring 1) input measurement errors and 2) possible state changes among historical measurements. While using the errors-in-variables model and letting the parameter and topology estimation interact with each other (PaToPa) can address input and output measurement error modeling, it only works when all measurements are from a single system state. To solve the two challenges simultaneously, we propose the “PaToPaEM” framework for joint line parameter and topology estimation with historical measurements from different unknown states. We improve the static framework that only works when measurements are from one single state, by further treating state changes in historical measurements as an unobserved latent variable. We then systematically analyze the new mathematical modeling, decouple the optimization problem, and incorporate the expectation-maximization (EM) algorithm to recover different hidden states in measurements. Combining these, the “PaToPaEM” framework enables joint topology and line parameter estimation using noisy measurements from multiple system states. It lays a solid foundation for data-driven system identification in distribution grids. Superior numerical results validate the practicability of the PaToPaEM framework.
TL;DR: In this article, a model identification method for hybrid systems is proposed, which is difficult to identify and analyse using classical dynamical systems theory. But the model identification methods largely focus on identifiability.
Abstract: Hybrid systems are traditionally difficult to identify and analyse using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identif...
TL;DR: Numerical results show the efficiency and robustness of the proposed MGS method-based VP algorithm, based on the modified Gram–Schmidt method, for separable nonlinear least-squares problems.
Abstract: Separable nonlinear models are very common in various research fields, such as machine learning and system identification. The variable projection (VP) approach is efficient for the optimization of such models. In this paper, we study various VP algorithms based on different matrix decompositions. Compared with the previous method, we use the analytical expression of the Jacobian matrix instead of finite differences. This improves the efficiency of the VP algorithms. In particular, based on the modified Gram–Schmidt (MGS) method, a more robust implementation of the VP algorithm is introduced for separable nonlinear least-squares problems. In numerical experiments, we compare the performance of five different implementations of the VP algorithm. Numerical results show the efficiency and robustness of the proposed MGS method-based VP algorithm.
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TL;DR: This paper proposes to learn compositional Koopman operators, using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects.
Abstract: Finding an embedding space for a linear approximation of a nonlinear dynamical system enables efficient system identification and control synthesis. The Koopman operator theory lays the foundation for identifying the nonlinear-to-linear coordinate transformations with data-driven methods. Recently, researchers have proposed to use deep neural networks as a more expressive class of basis functions for calculating the Koopman operators. These approaches, however, assume a fixed dimensional state space; they are therefore not applicable to scenarios with a variable number of objects. In this paper, we propose to learn compositional Koopman operators, using graph neural networks to encode the state into object-centric embeddings and using a block-wise linear transition matrix to regularize the shared structure across objects. The learned dynamics can quickly adapt to new environments of unknown physical parameters and produce control signals to achieve a specified goal. Our experiments on manipulating ropes and controlling soft robots show that the proposed method has better efficiency and generalization ability than existing baselines.
TL;DR: It is found that a difference of up to 20% in cooling cost for the cases studied can occur between the best performing model and the worst performing model, and the primary factors attributing to this were model structure and initial parameter guesses during parameter estimation of the model.
TL;DR: The paper outlines the key challenges inherent with system identification for power electronic applications; speed of estimation, computational complexity, estimation accuracy, tracking capability, and robustness to disturbances and time-varying systems.
Abstract: System identification is fundamental in many recent state-of-the-art developments in power electronic such as modeling, parameter tracking, estimation, self-tuning and adaptive control, health monitoring, and fault detection. Therefore, this paper presents a comprehensive review of parametric, non-parametric, and dual hybrid system identification for dc–dc switch mode power converter (SMPC) applications. The paper outlines the key challenges inherent with system identification for power electronic applications; speed of estimation, computational complexity, estimation accuracy, tracking capability, and robustness to disturbances and time-varying systems. Based on the literature in the field, modern solutions to these challenges are discussed in detail. Furthermore, this paper reviews and discusses the various applications of system identification for SMPCs; including health monitoring and fault detection.
TL;DR: In this paper, the authors present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics.
TL;DR: In this paper, a multidimensional approximation of nonlinear dynamical systems (MANDy) is proposed, which combines data-driven methods with tensor network decompositions.
Abstract: A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only There is a wide range of application areas for this important instance of system identification, ranging from industrial engineering and acoustic signal processing to stock market models In order to find appropriate representations of underlying dynamical systems, various data-driven methods have been proposed by different communities However, if the given data sets are high-dimensional, then these methods typically suffer from the curse of dimensionality To significantly reduce the computational costs and storage consumption, we propose the method multidimensional approximation of nonlinear dynamical systems (MANDy) which combines data-driven methods with tensor network decompositions The efficiency of the introduced approach will be illustrated with the aid of several high-dimensional nonlinear dynamical systems
TL;DR: A model switching estimation algorithm that online selects the most suitable model from its model library based on the relationship between load conditions for calibration and in practice that is able to reproduce SoC trajectories under various operating profiles.