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This paper is concerned with a problem of robust filtering for a finite-dimensional linear discrete time invariant system with two output signals, one of which is directly observed while the other has to be estimated. The system is assumed…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of a simplified semilinear gradient enhanced damage model. The model equations are of a special structure as the state equation…
A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
In this paper, we study the problem of estimating the state of a dynamic state-space system where the output is subject to quantization. We compare some classical approaches and a new development in the literature to obtain the filtering…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…
This paper proposes a resilient state estimator for LTI discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a…
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
We prove that for linear, discrete, time-varying, deterministic system (perfect model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance…
In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate…
For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…
This paper deals with the problem of state estimation for a class of linear time-invariant systems with quadratic output measurements. An immersion-type approach is presented that transforms the system into a state-affine system by adding a…
Distributed sensor networks often include a multitude of sensors, each measuring parts of a process state space or observing the operations of a system. Communication of measurements between the sensor nodes and estimator(s) cannot…
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…
This paper considers the Linear Minimum Variance recursive state estimation for the linear discrete time dynamic system with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is shown…
State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter,…
We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on…
The Kalman filter is indispensable for state estimation across diverse fields but faces computational challenges with higher dimensions. Approaches such as Riccati equation approximations aim to alleviate this complexity, yet ensuring…