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The Kalman(-Bucy) filter is the natural choice for the state reconstruction of disturbed, linear dynamical systems based on flawed and incomplete measurements. Taking a deterministic viewpoint this work investigates possible extensions of…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…
Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original…
State estimation or filtering serves as a fundamental task to enable intelligent decision-making in applications such as autonomous vehicles, robotics, healthcare monitoring, smart grids, intelligent transportation, and predictive…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
The Kalman filter is an algorithm for the estimation of hidden variables in dynamical systems under linear Gauss-Markov assumptions with widespread applications across different fields. Recently, its Bayesian interpretation has received a…
The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the choice of lifting…
This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…
Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…
We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…
Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. In this paper we propose a smoothing approach regularized by a quasilinearized ODE-based penalty in…
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, we focus on activating only a few sensors, among many available, to estimate the state of a stochastic process of interest. This problem is important in applications such as target tracking and simultaneous localization and…
This paper introduces new model parameterizations for learning discrete-time dynamical systems from data via the Koopman operator and studies their properties. Whereas most existing works on Koopman learning do not take into account the…
State estimation in heavy-tailed process and measurement noise is an important challenge that must be addressed in, e.g., tracking scenarios with agile targets and outlier-corrupted measurements. The performance of the Kalman filter (KF)…
This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…
Agnostic learning of Boolean halfspaces is a fundamental problem in computational learning theory, but it is known to be computationally hard even for weak learning. Recent work [CKKMK24] proposed smoothed analysis as a way to bypass such…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…