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Seminar za primijenjenu matematiku i teoriju upravljanja

 Ivan Veselić: Upper and lower Lipschitz bounds for perturbation of the edges of the essential spectr

29. VIII. 2019.

Ivan Veselić: Upper and lower Lipschitz bounds for perturbation of the edges of the essential spectrum

Abstract:Periodic Schroedinger operators have spectrum consisting of closed intervals as connected components. These are called spectral bands. They correspond to energies where transport is possible in the medium modelled by the Schroedinger operator. For this reason it is of interest to study perturbation of spectral bands. On the one hand, one wants to establish that for small perturbations the band will not move too much. On the other hand, for perturbations with fixed sign it possible to ensure that band edges will indeed move by a quantifiable amount. This makes spectral engineering possible. We report on such results based on unique continuation principles and variational principles for eigenvalues in gaps of the essential spectrum.

Juš Kocijan: Experimental probabilistic modelling of air pollution

21.III.2019.

Juš Kocijan: Experimental probabilistic modelling of air pollution

Abstract: The Gaussian-process model is a probabilistic, kernel-regression model that can be used for the identification of nonlinear dynamic systems.  A prediction of the Gaussian-process model, in addition to the mean value, also provides information about the confidence of the prediction using the prediction variance. Its modelling methodology incorporates various methods for modelling of different kinds of systems, among them online-, sparse-, deep- and other modelling methods. Recently these methods have been used for empirical modelling of different dynamic systems related to air quality. The lecture focuses on application and comparative assessment of different Gaussian-process modelling methods applied to air-quality problems. Presented case studies comprise modelling local ozone pollution and modelling of some atmospheric variables.

Vicko Prkačin: State and parameter estimation in aerial load manipulation

20.II.2019.

Vicko Prkačin: State and parameter estimation in aerial load manipulation

Abstract: State and parameter estimation in nonlinear systems is a challenging research topic. To date, there is no general solution for the state and parameter estimation of the nonlinear system which makes it an active field of research. Although there is no general ’go-to’ method, some methods are widely used. The extended Kalman filter is one of them. Despite being popular, it suffers from major drawbacks mostly caused by linearization which is overcome by development of unscented Kalman filter. In this paper these two methods are described alongside with least square estimation and estimation based on disturbance observer. Application to state and parameter estimation of the unmanned aerial vehicle (UAV) with suspended load is presented which due to the complexity of the nonlinear dynamics, present many challenges from the control point of view. One of the biggest are the oscillations caused by the swinging load that may bring system into self-oscillations and instability. To deal with this challenge, position of the slung load relative to the aircraft must be determined. This is the main focus of the current research and this paper.

Index Terms—State and parameter estimation, aerial load manipulation, nonlinear estimation, disturbance observer.


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