295,326 research outputs found
Convergence analysis of a family of robust Kalman filters based on the contraction principle
In this paper we analyze the convergence of a family of robust Kalman
filters. For each filter of this family the model uncertainty is tuned
according to the so called tolerance parameter. Assuming that the corresponding
state-space model is reachable and observable, we show that the corresponding
Riccati-like mapping is strictly contractive provided that the tolerance is
sufficiently small, accordingly the filter converges
Quantum risk-sensitive estimation and robustness
This paper studies a quantum risk-sensitive estimation problem and
investigates robustness properties of the filter. This is a direct extension to
the quantum case of analogous classical results. All investigations are based
on a discrete approximation model of the quantum system under consideration.
This allows us to study the problem in a simple mathematical setting. We close
the paper with some examples that demonstrate the robustness of the
risk-sensitive estimator.Comment: 24 page
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Generalized Stochastic Gradient Learning
We study the properties of generalized stochastic gradient (GSG) learning in forwardlooking models. We examine how the conditions for stability of standard stochastic gradient (SG) learning both di1er from and are related to E-stability, which governs stability under least squares learning. SG algorithms are sensitive to units of measurement and we show that there is a transformation of variables for which E-stability governs SG stability. GSG algorithms with constant gain have a deeper justification in terms of parameter drift, robustness and risk sensitivity
Model Predictive Control meets robust Kalman filtering
Model Predictive Control (MPC) is the principal control technique used in
industrial applications. Although it offers distinguishable qualities that make
it ideal for industrial applications, it can be questioned its robustness
regarding model uncertainties and external noises. In this paper we propose a
robust MPC controller that merges the simplicity in the design of MPC with
added robustness. In particular, our control system stems from the idea of
adding robustness in the prediction phase of the algorithm through a specific
robust Kalman filter recently introduced. Notably, the overall result is an
algorithm very similar to classic MPC but that also provides the user with the
possibility to tune the robustness of the control. To test the ability of the
controller to deal with errors in modeling, we consider a servomechanism system
characterized by nonlinear dynamics
Eco-labeling, rents, sales prices and occupancy rates: do LEED and Energy Star labeled offices obtain multiple premiums?
Drawing upon an updated and expanded dataset of Energy Star and LEED labeled commercial offices, this paper investigates the effect of eco-labeling on rental rates, sale prices and occupancy rates. Using OLS and robust regression procedures, hedonic modeling is used to test whether the presence of an eco-label has a significant positive effect on rental rates, sale prices and occupancy rates. The study suggests that estimated coefficients can be sensitive to outlier treatment. For sale prices and occupancy rates, there are notable differences between estimated coefficients for OLS and robust regressions. The results suggest that both Energy Star and LEED offices obtain rental premiums of approximately 3%. A 17% sale price premium is estimated for Energy Star labeled offices but no significant sale price premium is estimated for LEED labeled offices. Surprisingly, no significant occupancy premium is estimated for Energy Star labeled offices and a negative occupancy premium is estimated for LEED labeled offices
Robust Kalman Filtering under Model Perturbations
We consider a family of divergence-based minimax approaches to perform robust
filtering. The mismodeling budget, or tolerance, is specified at each time
increment of the model. More precisely, all possible model increments belong to
a ball which is formed by placing a bound on the Tau-divergence family between
the actual and the nominal model increment. Then, the robust filter is obtained
by minimizing the mean square error according to the least favorable model in
that ball. It turns out that the solution is a family of Kalman like filters.
Their gain matrix is updated according to a risk sensitive like iteration where
the risk sensitivity parameter is now time varying. As a consequence, we also
extend the risk sensitive filter to a family of risk sensitive like filters
according to the Tau-divergence family
Second Order Backward Stochastic Differential Equations with Quadratic Growth
We extend the wellposedness results for second order backward stochastic
differential equations introduced by Soner, Touzi and Zhang \cite{stz} to the
case of a bounded terminal condition and a generator with quadratic growth in
the variable. More precisely, we obtain uniqueness through a representation
of the solution inspired by stochastic control theory, and we obtain two
existence results using two different methods. In particular, we obtain the
existence of the simplest purely quadratic 2BSDEs through the classical
exponential change, which allows us to introduce a quasi-sure version of the
entropic risk measure. As an application, we also study robust risk-sensitive
control problems. Finally, we prove a Feynman-Kac formula and a probabilistic
representation for fully nonlinear PDEs in this setting.Comment: 31 page
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