The thesis will focus on the parameter and/or state estimation of stochastic models. In them, the noise is described by a probability distribution with a bounded support. These models will be used for prediction and model-based control.
The mentioned models are suitable for the description of real systems where some of the involved quantities are physically bounded, e.g., inherent non-negativity, a maximal allowed speed, etc.
There is a menu of varying options in this topic, such as comparing and testing different approaches to bounded quantities modelling, designing estimation algorithms or utilising the bounded state estimators in model predictive control.
Algorithms will be created in Matlab or C++.
[1] A. d’Onofrio, Bounded noises in physics, biology, and engineering. New York, Springer, 2013
[2] M. Kárný etal.: Optimized Bayesian Dynamic Advising: Theory and Algorithms, Springer, 2006
[3] M. S. Grewal, A. P. Andrews: Kalman Filtering – Theory and Practice Using MATLAB, 2008, Wiley-IEEE Press
[4] G. C. Goodwin, M. M. Seron and J. A. De Dona: Constrained Control and Estimation – An Optimisation Approach, Springer, 2005
[5] S. Kotz, J. R. Van Dorp: Beyond Beta – Other Continuous Families of Distributions with Bounded Support and Applications, World Scientific Publishing, 2004
[6] Complementary options according to a specific problem formulation.
