Showing papers on "System identification published in 2021"

Noise-Immune Model Identification and State-of-Charge Estimation for Lithium-Ion Battery Using Bilinear Parameterization

Abstract: Accurate estimation of state of charge (SOC) is critical to the safe and efficient utilization of a battery system. Model-based SOC observers have been widely used due to their high accuracy and robustness, but they rely on a well-parameterized battery model. This article scrutinizes the effect of measurement noises on model parameter identification and SOC estimation. A novel parameterization method combining instrumental variable (IV) estimation and bilinear principle is proposed to compensate for the noise-induced biases of model identification. Specifically, the IV estimator is used to reformulate an overdetermined system so as to allow coestimating the model parameters and noise variances. The coestimation problem is then decoupled into two linear subproblems which are solved efficiently by a two-stage least squares algorithm in a recursive manner. The parameterization method is further combined with a Luenberger observer to estimate the SOC in real time. Simulations and experiments are performed to validate the proposed method. Results reveal that the proposed method is superior to existing method in terms of the immunity to noise corruption.

Data-Driven Control of Soft Robots Using Koopman Operator Theory

Abstract: Controlling soft robots with precision is a challenge due to the difficulty of constructing models that are amenable to model-based control design techniques. Koopman operator theory offers a way to construct explicit dynamical models of soft robots and to control them using established model-based control methods. This approach is data driven, yet yields an explicit control-oriented model rather than just a “black-box” input–output mapping. This work describes a Koopman-based system identification method and its application to model predictive control (MPC) design for soft robots. Three MPC controllers are developed for a pneumatic soft robot arm via the Koopman-based approach, and their performances are evaluated with respect to several real-world trajectory following tasks. In terms of average tracking error, these Koopman-based controllers are more than three times more accurate than a benchmark MPC controller based on a linear state-space model of the same system, demonstrating the utility of the Koopman approach in controlling real soft robots.

Iterative identification methods for a class of bilinear systems by using the particle filtering technique

Abstract: Summary This article mainly studies the iterative parameter estimation problems of a class of nonlinear systems. Based on the auxiliary model identification idea, this article utilizes the estimate...

New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-Time Cases

Abstract: We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include the following, first, a unified treatment of the continuous and the discrete-time cases; second, the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement , and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and, third, an alternative estimator ensuring convergence in finite-time whose adaptation gain, in contrast with the existing one, does not converge to zero. Simulations that illustrate our results are also presented.

Gray-Box Parsimonious Subspace Identification of Hammerstein-Type Systems

Abstract: In this article, a gray-box parsimonious subspace identification method using sampled dynamical and steady-state data is proposed for block-oriented Hammerstein-type systems. Compared with the conventional subspace identification methods based on over-parameterized models, the proposed method assumes parsimonious models, where the number of parameters is as minimal as possible to ensure the model accuracy, especially for highly nonlinear models. Generally, the available dynamical data do not contain adequate information on the low-frequency characteristics of the system. To improve the accuracy of model identification, the steady-state information of the system is taken into account, and a multiregularization method is developed, where the whole model parameters are estimated in a hierarchical, iterative manner from two sets of data: the dynamical input–output data and the steady-state input–output data. The use of parsimonious models and hierarchical estimation can significantly reduce the size of the associated parameter estimation error covariance matrix, thus improving the model accuracy and decreasing the variance of the estimated parameters, compared with the over-parametrization methods only using dynamical data. The effectiveness and merits are demonstrated by a simulation example and a real-world example.

Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches.

Abstract: Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. This manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

Bridging direct & indirect data-driven control formulations via regularizations and relaxations

Abstract: We discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data-driven control approach seeking an optimal decision compatible with recorded data assembled in a Hankel matrix and robustified through suitable regularizations. We formulate these two problems in the language of behavioral systems theory and parametric mathematical programs, and we bridge them through a multi-criteria formulation trading off system identification and control objectives. We illustrate our results with two methods from subspace identification and control: namely, subspace predictive control and low-rank approximation which constrain trajectories to be consistent with a non-parametric predictor derived from (respectively, the column span of) a data Hankel matrix. In both cases we conclude that direct and regularized data-driven control can be derived as convex relaxation of the indirect approach, and the regularizations account for an implicit identification step. Our analysis further reveals a novel regularizer and a plausible hypothesis explaining the remarkable empirical performance of direct methods on nonlinear systems.

Underwater Soft Robot Modeling and Control With Differentiable Simulation

Abstract: Underwater soft robots are challenging to model and control because of their high degrees of freedom and their intricate coupling with water. In this letter, we present a method that leverages the recent development in differentiable simulation coupled with a differentiable, analytical hydrodynamic model to assist with the modeling and control of an underwater soft robot. We apply this method to Starfish, a customized soft robot design that is easy to fabricate and intuitive to manipulate. Our method starts with data obtained from the real robot and alternates between simulation and experiments. Specifically, the simulation step uses gradients from a differentiable simulator to run system identification and trajectory optimization, and the experiment step executes the optimized trajectory on the robot to collect new data to be fed into simulation. Our demonstration on Starfish shows that proper usage of gradients from a differentiable simulator not only narrows down its simulation-to-reality gap but also improves the performance of an open-loop controller in real experiments.

Data-enabled predictive control for quadcopters

Abstract: We study the application of a data-enabled predictive control (DeePC) algorithm for position control of real-world nano-quadcopters. The DeePC algorithm is a finite-horizon, optimal control method that uses input/output measurements from the system to predict future trajectories without the need for system identification or state estimation. The algorithm predicts future trajectories of the quadcopter by linearly combining previously measured trajectories (motion primitives). We illustrate the necessity of a regularized variant of the DeePC algorithm to handle the nonlinear nature of the real-world quadcopter dynamics with noisy measurements. Simulation-based analysis is used to gain insights into the effects of regularization, and experimental results validate that these insights carry over to the real-world quadcopter. Moreover, we demonstrate the reliability of the DeePC algorithm by collecting a new set of input/output measurements for every real-world experiment performed. The performance of the DeePC algorithm is compared to Model Predictive Control based on a first-principles model of the quadcopter. The results are demonstrated with a video of successful trajectory tracking of the real-world quadcopter.

Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

Abstract: In this paper, an adaptive dynamic programming (ADP) strategy is investigated for discrete-time nonlinear systems with unknown nonlinear dynamics subject to input saturation. To save the communication resources between the controller and the actuators, stochastic communication protocols (SCPs) are adopted to schedule the control signal, and therefore the closed-loop system is essentially a protocol-induced switching system. A neural network (NN)-based identifier with a robust term is exploited for approximating the unknown nonlinear system, and a set of switch-based updating rules with an additional tunable parameter of NN weights are developed with the help of the gradient descent. By virtue of a novel Lyapunov function, a sufficient condition is proposed to achieve the stability of both system identification errors and the update dynamics of NN weights. Then, a value iterative ADP algorithm in an offline way is proposed to solve the optimal control of protocol-induced switching systems with saturation constraints, and the convergence is profoundly discussed in light of mathematical induction. Furthermore, an actor-critic NN scheme is developed to approximate the control law and the proposed performance index function in the framework of ADP, and the stability of the closed-loop system is analyzed in view of the Lyapunov theory. Finally, the numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Deep Learning-Based Model Predictive Control for Continuous Stirred-Tank Reactor System

Abstract: A continuous stirred-tank reactor (CSTR) system is widely applied in wastewater treatment processes. Its control is a challenging industrial-process-control problem due to great difficulty to achieve accurate system identification. This work proposes a deep learning-based model predictive control (DeepMPC) to model and control the CSTR system. The proposed DeepMPC consists of a growing deep belief network (GDBN) and an optimal controller. First, GDBN can automatically determine its size with transfer learning to achieve high performance in system identification, and it serves just as a predictive model of a controlled system. The model can accurately approximate the dynamics of the controlled system with a uniformly ultimately bounded error. Second, quadratic optimization is conducted to obtain an optimal controller. This work analyzes the convergence and stability of DeepMPC. Finally, the DeepMPC is used to model and control a second-order CSTR system. In the experiments, DeepMPC shows a better performance in modeling, tracking, and antidisturbance than the other state-of-the-art methods.

Time Series Anomaly Detection for Cyber-physical Systems via Neural System Identification and Bayesian Filtering

Abstract: Recent advances in AIoT technologies have led to an increasing popularity of utilizing machine learning algorithms to detect operational failures for cyber-physical systems (CPS). In its basic form, an anomaly detection module monitors the sensor measurements and actuator states from the physical plant, and detects anomalies in these measurements to identify abnormal operation status. Nevertheless, building effective anomaly detection models for CPS is rather challenging as the model has to accurately detect anomalies in presence of highly complicated system dynamics and unknown amount of sensor noise. In this work, we propose a novel time series anomaly detection method called Neural System Identification and Bayesian Filtering (NSIBF) in which a specially crafted neural network architecture is posed for system identification, i.e., capturing the dynamics of CPS in a dynamical state-space model; then a Bayesian filtering algorithm is naturally applied on top of the "identified" state-space model for robust anomaly detection by tracking the uncertainty of the hidden state of the system recursively over time. We provide qualitative as well as quantitative experiments with the proposed method on a synthetic and three real-world CPS datasets, showing that NSIBF compares favorably to the state-of-the-art methods with considerable improvements on anomaly detection in CPS.

A Convex Parameterization of Robust Recurrent Neural Networks

Abstract: Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many applications. In this letter, we formulate convex sets of RNNs with stability and robustness guarantees. The guarantees are derived using incremental quadratic constraints and can ensure global exponential stability of all solutions, and bounds on incremental $\ell _{2} $ gain (the Lipschitz constant of the learned sequence-to-sequence mapping). Using an implicit model structure, we construct a parametrization of RNNs that is jointly convex in the model parameters and stability certificate. We prove that this model structure includes all previously-proposed convex sets of stable RNNs as special cases, and also includes all stable linear dynamical systems. Numerical experiments illustrate the utility of the proposed model class in the context of non-linear system identification.

Promoting global stability in data-driven models of quadratic nonlinear dynamics

Abstract: Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the global stability (i.e., long-time boundedness) of these models. In this work, we illustrate how to modify the objective function in machine learning algorithms to promote globally stable data-driven models of fluid and plasma flows. This innovation significantly extends the applicability of sparse system identification for complex dynamics, such as models of turbulent boundary layers.

Recursive Variable Projection Algorithm for a Class of Separable Nonlinear Models

Abstract: In this article, we study the recursive algorithms for a class of separable nonlinear models (SNLMs) in which the parameters can be partitioned into a linear part and a nonlinear part. Such models are very common in machine learning, system identification, and signal processing. Utilizing the special structure of the SNLMs, we propose a recursive variable projection (RVP) algorithm, in which at each recursion, the linear parameters of the model are eliminated, and the nonlinear parameters are updated by the recursive Levenberg–Marquart algorithm. Then, based on the updated nonlinear parameters, the linear parameters are updated by the recursive least-squares algorithm. According to a convergence analysis of the RVP algorithm, the parameter estimation error is mean-square bounded. Numerical examples confirm the satisfactory performance of the proposed algorithm.

Time Series Anomaly Detection for Cyber-physical Systems via Neural System Identification and Bayesian Filtering

Abstract: Recent advances in AIoT technologies have led to an increasing popularity of utilizing machine learning algorithms to detect operational failures for cyber-physical systems (CPS). In its basic form, an anomaly detection module monitors the sensor measurements and actuator states from the physical plant, and detects anomalies in these measurements to identify abnormal operation status. Nevertheless, building effective anomaly detection models for CPS is rather challenging as the model has to accurately detect anomalies in presence of highly complicated system dynamics and unknown amount of sensor noise. In this work, we propose a novel time series anomaly detection method called Neural System Identification and Bayesian Filtering (NSIBF) in which a specially crafted neural network architecture is posed for system identification, i.e., capturing the dynamics of CPS in a dynamical state-space model; then a Bayesian filtering algorithm is naturally applied on top of the "identified" state-space model for robust anomaly detection by tracking the uncertainty of the hidden state of the system recursively over time. We provide qualitative as well as quantitative experiments with the proposed method on a synthetic and three real-world CPS datasets, showing that NSIBF compares favorably to the state-of-the-art methods with considerable improvements on anomaly detection in CPS.

Joint Logarithmic Hyperbolic Cosine Robust Sparse Adaptive Algorithms

Abstract: Recently, the logarithmic hyperbolic cosine adaptive filter (LHCAF) was proposed and was seen to demonstrate excellent robustness against impulsive interference. However, for the modelling of sparse systems, it may not provide optimal performance as it does not take into account the sparse nature of the system. To improve the modelling accuracy and convergence performance, a sparsity aware zero attraction LHCAF (ZA-LHCAF) and a reweighted zero attraction LHCAF (RZA-LHCAF) is proposed. To further improve the performance for modelling of sparse systems in impulsive environments, a joint logarithmic hyperbolic cosine function (JLHCF) is proposed as the cost function. The corresponding update rule, called the joint logarithmic hyperbolic cosine adaptive filter (JLHCAF) is deduced and the bound on learning rate is derived. A room equalization scenario is also considered and an improved sparsity aware robust algorithm based on JLHCF, namely the filtered-x JLHCAF (Fx-JLHCAF) is proposed for the same. Extensive simulation studies carried out for different system identification scenarios, under Gaussian and non-Gaussian disturbances and a room equalization scenario, demonstrate the superior performance achieved by JLHCAF over existing sparsity aware robust adaptive filters.

PySINDy: A comprehensive Python package for robust sparse system identification

Abstract: Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.

Identification and U-control of a state-space system with time-delay

Abstract: This article presents a state-space model with time-delay to map the relationship between known input-output data for discrete systems. For the given input-output data, a model identification algorithm combining parameter estimation and state estimation is proposed in line with the causality constraints. Consequently, this article proposes a least squares parameter estimation algorithm, and analyzes its convergence for the studied systems to prove that the parameter estimation errors converge to zero under the persistent excitation conditions. In control system design, the U-model based control is introduced to provide a unilateral platform to improve the design efficiency and generality. A simulation portfolio from modeling to control is provided with computational experiments to validate the derived results.

RNN- and LSTM-Based Soft Sensors Transferability for an Industrial Process.

Abstract: The design and application of Soft Sensors (SSs) in the process industry is a growing research field, which needs to mediate problems of model accuracy with data availability and computational complexity. Black-box machine learning (ML) methods are often used as an efficient tool to implement SSs. Many efforts are, however, required to properly select input variables, model class, model order and the needed hyperparameters. The aim of this work was to investigate the possibility to transfer the knowledge acquired in the design of a SS for a given process to a similar one. This has been approached as a transfer learning problem from a source to a target domain. The implementation of a transfer learning procedure allows to considerably reduce the computational time dedicated to the SS design procedure, leaving out many of the required phases. Two transfer learning methods have been proposed, evaluating their suitability to design SSs based on nonlinear dynamical models. Recurrent neural structures have been used to implement the SSs. In detail, recurrent neural networks and long short-term memory architectures have been compared in regard to their transferability. An industrial case of study has been considered, to evaluate the performance of the proposed procedures and the best compromise between SS performance and computational effort in transferring the model. The problem of labeled data scarcity in the target domain has been also discussed. The obtained results demonstrate the suitability of the proposed transfer learning methods in the design of nonlinear dynamical models for industrial systems.