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.

Linear Hall sensors are a cost-effective alternative to optical encoders for measuring the rotor positions of actuators, with the main challenge being that they exhibit position-dependent inaccuracies resulting from manufacturing tolerances. This paper develops a data-driven calibration procedure for linear analog Hall sensors that enables accurate online estimates of the rotor angle without requiring expensive external encoders. The approach combines closed-loop data collection with nonlinear identification to obtain an accurate model of the sensor inaccuracies, which is subsequently used for online compensation. Simulation results show that when the flux density model structure is known, measurement errors are reduced to the sensor noise floor, and experiments on an industrial setup demonstrate a factor of 2.6 reduction in the root-mean-square measurement error. These results confirm that Hall sensor inaccuracies can be calibrated even when no external encoder is available, improving their practical applicability.

Hysteresis is a ubiquitous phenomenon in magnetic materials; its modeling and identification are crucial for understanding and optimizing the behavior of electrical machines. Such machines often operate under uncertain conditions, necessitating modeling methods that can generalize across unobserved scenarios. Traditional recurrent neural architectures struggle to generalize hysteresis patterns beyond their training domains. This paper mitigates the generalization challenge by introducing a physics-aware recurrent neural network approach to model and generalize the hysteresis manifesting in sequentiality and history-dependence. The proposed method leverages ordinary differential equations (ODEs) governing the phenomenological hysteresis models to update hidden recurrent states. The effectiveness of the proposed method is evaluated by predicting generalized scenarios, including first-order reversal curves and minor loops. The results demonstrate robust generalization to previously untrained regions, even with noisy data, an essential feature that hysteresis models must have. The results highlight the advantages of integrating physics-based ODEs into recurrent architectures, including superior performance over traditional methods in capturing the complex, nonlinear hysteresis behaviors in magnetic materials.

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.

Nonlinear hysteresis modeling is essential for estimating, controlling, and characterizing the behavior of piezoelectric material-based devices. However, current deep-learning approaches face challenges in generalizing effectively to previously unseen voltage profiles. This Letter tackles the limitation of generalization by introducing the notion of neural operators for modeling the nonlinear constitutive laws governing inverse piezoelectric hysteresis, specifically focusing on the relationship between voltage inputs and displacement responses. The study utilizes two neural operators—Fourier neural operator and the deep operator network—to predict material responses to unseen voltage profiles that are not part of the training data. Numerical experiments, including butterfly-shaped hysteresis curves, show that in accuracy and generalization to unseen voltage profiles, neural operators outperform traditional recurrent neural network-based models, including conventional gated networks. The findings highlight the potential of neural operators for modeling hysteresis in piezoelectric materials, offering advantages over existing methods in varying voltage scenarios.

Optimal input design plays an important role in system identification for complex and multivariable systems. A known paradox in input design is that the optimal inputs depend on the true but unknown system. The aim of this paper is to design inputs for multivariable systems that are robust to all system variations within a given continuous uncertainty set. In the presented approach, the robust design problem is cast as an infinite-dimensional min-max optimization problem, and tackled via the S-lemma in an iterative approximation scheme. Experimental results from a multivariable motion system show that the algorithm enables significant robustness improvements.

Control applications are increasingly sampled non-equidistantly in time, including in motion control, networked control, resource-aware control, and event-triggered control. Some of these applications use measurement devices that sample equidistantly in the amplitude domain. The aim of this paper is to develop a non-parametric estimator of the impulse response of continuous-time systems based on such sampling strategy, known as Lebesgue-sampling. To this end, kernel methods are developed to formulate an algorithm that adequately takes into account the output intersample behavior, which ultimately leads to more accurate models and more efficient output sampling compared to the standard approach. The efficacy of this method is demonstrated through a mass-spring damper case study.

Frequency Response Matrix (FRM) estimation from measured data is an important step towards the control of complex systems, including motion and thermal systems. Missing samples in the measured data records, e.g., due to sensor failure or faulty data transmission, often occur. In this paper, a method is presented for the nonparametric FRM identification of multiple-inputs multiple-outputs (MIMO) systems from incomplete and noisy data records. The method exploits time- and frequency-domain localizing wavelets to accurately estimate the FRM and its covariance from the time-frequency plane. Good performance is demonstrated in a simulation study.

Frequency response function (FRF) estimation from measured data is an essential step in the design, control, and analysis of complex dynamical systems, including thermal and motion systems. Especially for systems that require long measurement time, missing samples in the data record, e.g., due to measurement interruptions, often occur. The aim of this article is to achieve accurate identification of nonparametric FRF models of periodically excited systems from noisy output measurements with missing samples. An identification framework is established that exploits a wavelet-based transform to separate the effect of the missing samples in the time domain from the system characteristics in tre frequency domain. The framework encompasses both a time-invariant and a time-varying wavelet-based estimator, which provides different mechanisms to address the missing samples. Experimental results from a thermodynamical system confirm that the estimators enable accurate identification.

Frequency Response Function (FRF) identification plays a crucial role in the design, the control, and the analysis of complex dynamical systems, including thermal and motion systems. Especially for applications that require long measurements, missing data samples, e.g., due to interruptions in the data transmission or sensor failure, often occur. The aim of this paper is to accurately identify nonparametric FRF models of periodically excited systems from noisy output measurements with missing samples. The presented method employs a wavelet-based transformation to address the identification problem in the time-frequency plane. A simulation example confirms that the developed techniques produce accurate estimates, even when many samples are missing.