Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard optimization algorithms for system identification usually fail. We present a new approach that combines the recent advances in physics-informed neural networks and the well-known achievements of Kalman filters in order to find parameters in a continuous-time system with noisy measurements. In doing so, our approach allows estimating the parameters together with the mean value and covariance matrix of the system's state vector. We show that the method works for complex systems by identifying the parameters of a double pendulum.
We consider the problem of estimating a continuous-time Gauss-Markov source process observed through a vector Gaussian channel with an adjustable channel gain matrix. For a given (generally time-varying) channel gain matrix, we provide formulas to compute (i) the mean-square estimation error attainable by the classical Kalman-Bucy filter, and (ii) the mutual information between the source process and its Kalman-Bucy estimate. We then formulate a novel "optimal channel gain control problem" where the objective is to control the channel gain matrix strategically to minimize the weighted sum of t…
This paper proposes a distributed secondary voltage control method based on extended state Kalman-Bucy filter (ESKBF) and fast terminal sliding mode (FTSM) control for the resilient operation of an islanded microgrid (MG) with inverter-based distributed generations (DGs). To tackle the co-existence of multiple uncertainties, a unified modelling framework is proposed to represent the set of different types of disturbances, including parameter perturbation, measurement noise, and immeasurably external variables, by an extended state method. Kalman-Bucy filter is then applied to accurately estima…
This paper proposes a novel vehicle sideslip angle estimator, which uses the physical knowledge from an Unscented Kalman Filter (UKF) based on a non-linear single-track vehicle model to enhance the estimation accuracy of a Convolutional Neural Network (CNN). The model-based and data-driven approaches interact mutually, and both use the standard inertial measurement unit and the tyre forces measured by load sensing technology. CNN benefits from the UKF the capacity to leverage the laws of physics. Concurrently, the UKF uses the CNN outputs as sideslip angle pseudo-measurement and adaptive proce…
This paper contributes to the emerging viewpoint that governing equations for dynamic state estimation, conditioned on the history of noisy measurements, can be viewed as gradient flow on the manifold of joint probability density functions with respect to suitable metrics. Herein, we focus on the Wonham filter where the prior dynamics is given by a continuous time Markov chain on a finite state space; the measurement model includes noisy observation of the (possibly nonlinear function of) state. We establish that the posterior flow given by the Wonham filter can be viewed as the small time-ste…
Weighted Flow Matching and Physics-Informed Nonlinear Filtering for Parameter Estimation in Digital Twins
Department of Applied Mathematics, University of California, Santa Cruz, CA 95064, USA（应用数学系，加州大学圣克鲁兹分校）；Department of Electrical and Computer Engineering, University of California, Santa Cruz, CA 95064, USA（电气与计算机工程系，加州大学圣克鲁兹分校）
We develop data-driven algorithms to fully automate sensor fault detection in systems governed by underlying physics. The proposed machine learning method uses a time series of typical behavior to approximate the evolution of measurements of interest by a linear time-invariant system. Given additional data from related sensors, a Kalman observer is used to maintain a separate real-time estimate of the measurement of interest. Sustained deviation between the measurements and the estimate is used to detect anomalous behavior. A decision tree, informed by integrating other sensor measurement valu…
Varying power-infeed from converter-based generation units introduces great uncertainty on system parameters such as inertia and damping. As a consequence, system operators face increasing challenges in performing dynamic security assessment and taking real-time control actions. Exploiting the widespread deployment of phasor measurement units (PMUs) and aiming at developing a fast dynamic state and parameter estimation tool, this paper investigates the performance of Physics-Informed Neural Networks (PINN) for discovering the frequency dynamics of future power systems. PINNs have the potential…
When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators for linear dynamical systems with $ε$ insensitive loss functions. The $ε$ insensitive loss function, which is often used in Support Vector Machines, provides greater robustness when the measurements are biased and very noisy as the algorithm tolerates small errors in prediction which in turn makes the estimates less sensitive to measurement noises. Apart from …
Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory
Institute of Mechatronic Systems, Leibniz University Hannover（机械系统研究所，汉诺威莱布尼茨大学）；Department of Advanced Interdisciplinary Studies, The University of Tokyo（先进跨学科研究部，东京大学）；Institute of Assembly Technology and Robotics, Leibniz University of Hannover（组装技术与机器人研究所，汉诺威莱布尼茨大学）
Advances in edge computing are powering the development and deployment of Internet of Things (IoT) systems to provide advanced services and resource efficiency. However, large-scale IoT-based load-altering attacks (LAAs) can seriously impact power grid operations, such as destabilising the grid's control loops. Timely detection and identification of any compromised nodes are essential to minimise the adverse effects of these attacks on power grid operations. In this work, two data-driven algorithms are proposed to detect and identify compromised nodes and the attack parameters of the LAAs. The…
