Advanced control strategies, and model predictive control (MPC) in particular, are gaining widespread interest for building climate control, since they can systematically save energy and/or costs with simultaneous thermal comfort improvement, as well as adapt the energy demand according to the available renewable/residual supply. As outlined in the previous topic, MPC however suffers from parametric uncertainties (p) and additive uncertainties (a) that substantially limit the performance of these approaches.
Several computational methods to handle uncertainties in mathematical models have recently been developed at KU Leuven; for example, quasi-Monte Carlo methods in forward uncertainty quantification for PDEs with random diffusion coefficients. Quasi-Monte Carlo methods are multivariate quadrature methods which are especially suitable for higher dimensional integrals/expectations, having the possibility of vanquishing the curse of dimensionality under certain conditions. These methods can also be used for inverse problems, such as determining parameters of a mathematical model given data, and for function approximation. In particular, Bayesian inversion allows the formulation of a point estimator for the parameters of a mathematical model in terms of (high-dimensional) integrals. If the mathematical model is relatively expensive then it can be approximated by a Gaussian process surrogate. The Gaussian process emulator can be interpreted as a kernel interpolation method for function approximation with added uncertainty. Recently new construction methods for quasi-Monte Carlo point sets for function approximation were developed which can also be used for kernel interpolation methods. Last but not least, in the dissertation of Van Barel at KUL, multilevel Monte Carlo and quasi-Monte Carlo methods were developed for robust optimization under uncertainty.
In this Ph.D. research, we aim to improve this methodology in direct, practical, application to optimal control problems in residential and commercial thermal energy management.
The PhD fellowship is granted within the collaboration between the University of Leuven and VITO.
The successful candidate will be supervised by Prof. Dirk Nuyens (KU Leuven) and co-promoted by Dr. Brida Mbuwir (VITO).
For more information, please contact Dr. Brida Mbuwir: firstname.lastname@example.org.
How to apply?
Applications should be submitted online and should include a copy of your CV and a cover letter.
The remainder of the selection procedure is specific to the position and will be determined by the selection panel.
You can apply for this PhD vacancy no later than September 5, 2022.
More information is available on PhD | VITO.