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Digital PID control requires a differencing operation to implement the D gain. In order to suppress the effects of noisy data, the traditional approach is to filter the data, where the frequency response of the filter is adjusted manually…

Extremum-seeking control (ESC) is widely used to optimize performance when the system dynamics are uncertain. However, sensitivity to sensor noise is a crucial issue in ESC implementation due to the use of high-pass filters or gradient…

Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…

Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor s angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process…

Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable…

Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…

Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are…

We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…

Reliable state estimation is essential for autonomous systems operating in complex, noisy environments. Classical filtering approaches, such as the Kalman filter, can struggle when facing nonlinear dynamics or non-Gaussian noise, and even…

Adaptive importance sampling (AIS) algorithms are a rising methodology in signal processing, statistics, and machine learning. An effective adaptation of the proposals is key for the success of AIS. Recent works have shown that gradient…

Determining physical properties inside an object without access to direct measurements of target regions can be formulated as a specific type of \textit{inverse problem}. One of such problems is applied in \textit{Electrical Impedance…

Robust training with noisy labels is a critical challenge in image classification, offering the potential to reduce reliance on costly clean-label datasets. Real-world datasets often contain a mix of in-distribution (ID) and…

Fast and robust dynamic state estimation (DSE) is essential for accurately capturing the internal dynamic processes of power systems, and it serves as the foundation for reliably implementing real-time dynamic modeling, monitoring, and…

Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the…

The accurate estimation of the noise covariance matrix (NCM) in a dynamic system is critical for state estimation and control, as it has a major influence in their optimality. Although a large number of NCM estimation methods have been…

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…

A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…

In this paper, a new data-adaptive method, called DAIS (Data Adaptive ISolation), is introduced for the estimation of the number and the location of change-points in a given data sequence. The proposed method can detect changes in various…

Recent works have shown that neural networks are vulnerable to carefully crafted adversarial examples (AE). By adding small perturbations to input images, AEs are able to make the victim model predicts incorrect outputs. Several research…

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…