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Seminar za primijenjenu matematiku i teoriju upravljanja

 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.

 Cesare Molinari: Generalized Conditional Gradient with Augmented Lagrangian

13.II.2019.

Cesare Molinari: Generalized Conditional Gradient with Augmented Lagrangian

Abstract. In this talk we discuss a splitting scheme which hybridizes generalized conditional gradient with a proximal step which we call CGAL algorithm, for minimizing the sum of three proper convex and lower-semicontinuous functions in real Hilbert spaces. The minimization is subject to an affine constraint, that allows in particular to deal with composite problems (sum of more than three functions) in a separate way by the usual product space technique. While classical conditional gradient methods require Lipschitz-continuity of the gradient of the differentiable part of the objective, CGAL needs only differentiability (on an appropriate subset), hence circumventing the intricate question of Lipschitz continuity of gradients. For the two remaining functions in the objective, we do not require any additional regularity assumption. The second function, possibly nonsmooth, is assumed simple, i.e., the associated proximal mapping is easily computable. For the third function, again nonsmooth, we just assume that its domain is also bounded and that a linearly perturbed minimization oracle is accessible. In particular, this last function can be chosen to be the indicator of a nonempty bounded closed convex set, in order to deal with additional constraints. Finally, the affine constraint is addressed by the augmented Lagrangian approach. Our analysis is carried out for a wide choice of algorithm parameters satisfying so called open loop rules. As main results, under mild conditions, we show asymptotic feasibility with respect to the affine constraint, boundedness of the dual multipliers, and convergence of the Lagrangian values to the saddle-point optimal value. We also provide (subsequential) rates of convergence for both the feasibility gap and the Lagrangian values.

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