Related papers: System Identification for Continuous-time Linear D…
While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the…
In this paper, we develop the mathematical framework for filtering problems arising from biophysical applications where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
Learning governing equations from data is central to understanding the behavior of physical systems across diverse scientific disciplines, including physics, biology, and engineering. The Sindy algorithm has proven effective in leveraging…
Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…
In this paper, we propose a new model reduction technique for linear stochastic systems that builds upon knowledge filtering and utilizes optimal Kalman filtering techniques. This new technique will reduce the dimension of the noise…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
This paper derives a \emph{distributed} Kalman filter to estimate a sparsely connected, large-scale, $n-$dimensional, dynamical system monitored by a network of $N$ sensors. Local Kalman filters are implemented on the ($n_l-$dimensional,…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
The work of Kalman and Bucy has established a duality between filtering and optimal estimation in the context of time-continuous linear systems. This duality has recently been extended to time-continuous nonlinear systems in terms of an…
The capability of a novel Kullback-Leibler divergence method is examined herein within the Kalman filter framework to select the input-parameter-state estimation execution with the most plausible results. This identification suffers from…
This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…
Despite the widespread usage of discrete generation Ensemble Kalman particle filtering methodology to solve nonlinear and high dimensional filtering and inverse problems, little is known about their mathematical foundations. As genetic-type…
This paper is concerned with the linear/nonlinear Kalman-like filtering problem under binary sensors. Since innovation represents new information in the sensor measurement and serves to correct the prediction for the Kalman-like filter…
In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any…
In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary…
This paper introduces a unified approach for state estimation and control of nonlinear dynamic systems, employing the State-Dependent Riccati Equation (SDRE) framework. The proposed approach naturally extends classical linear quadratic…
We propose a new extension of Kalman filtering for continuous-discrete systems with nonlinear state-space models that we name as the level set Kalman filter (LSKF). The LSKF assumes the probability distribution can be approximated as a…
In this paper, we present a methodology to identify discrete-time state-space switched linear systems (SLSs) from input-output measurements. Continuous-state is not assumed to be measured. The key step is a deadbeat observer based…
This paper presents a discrete-time nonlinear system identification method while satisfying the stability and safety properties of the system with high probability. An Extreme Learning Machine (ELM) is used with a Gaussian assumption on the…