For dynamic processes where only approximate models are available, data-driven strategies that adapt the model and/or the control problem formulation online need to be employed in order to ensure optimal control performance. On the one hand, the system model might include white-box parameters, i.e. some constants within a physical model, that are not known exactly or might change over the course of operation. On the other hand, if the system exhibits behaviour for which no exact model is known or the available models are too computationally demanding to be used within a feedback control system, one might introduce additional black-box parameters. These parameters do not have a physical interpretation, but allow for a model correction in order to (locally or globally) explain the observed system behaviour. The focus of my PhD is to develop optimal control and estimation problem formulations as well as numerical algorithms to efficiently identify unknown white-box parameters as well as black-box model corrections from data leading to adaptive optimal control strategies.
For estimation of white-box parameters, Moving Horizon Estimation (MHE) is a powerful framework that allows us to explicitly account for various noise distributions and additional nonlinear constraints. The main challenge for applying MHE in practice is its computational complexity. As part of my PhD,
I have been exploring tailored algorithms that exploit the particular structure of the MHE problem or use approximate formulations. Future research will include formulations with non-Gaussian noise distributions leading to non-convex loss functions for which specialized numerical optimization
methods can be leveraged.
If models with black-box components are used, it can be advantageous to explicitly take into account the control problem formulation to identify those parts of the state space where the cost function is highly sensitive to modeling errors and, maybe even more importantly, where it is not affected
by small changes of the model equations. Future research will include algorithms for active system identification that exploit the structure of the optimal control problem at hand when selecting those directions in the state space in which the system behaviour is to be explored.