A very brief summary for each of the three topics mentioned above follows. The results can be found in peer-reviewed original research papers.
Battery management systems (BMSs):
Batteries degrade over time, so a BMS should maximize the benefits obtained from using the battery over its lifetime. However, the degradation rate depends on its use. This leads to stochastic optimal control problems of a certain mathematical form. Initially, this mathematical problem was studied and efficient solution algorithms were proposed. These algorithms were applied to a BMS performing frequency regulation, assuming a simplified model. The research then focused on Li-ion batteries and used more accurate degradation models. A two-time-scale approach was used to solve the problem. Some considerations on the mathematical form of the solution allow for important computational efficiency improvements. Finally, we used a simplified physics-based model for battery aging, together with more realistic economic considerations. Suitable techniques from optimal control theory were used to solve this problem.
Autonomous vehicles:
We studied a distributed hierarchical control strategy for fleets of autonomous vehicles cruising on a highway with diverse desired speeds. The goal is to design a control scheme that can be employed when only vehicle-to-vehicle communication is available and vehicles need to negotiate and agree on their positions on the road. Suitable algorithms have been developed. Also, problems of two vehicles crossing an intersection have been studied. Under suitable assumptions, the optimal braking/reaccelerating speed profile is found for the vehicle crossing second. The main criterion is the time loss by this vehicle due to braking and reaccelerating. All solutions are in closed form.
Parameter identification and application to tumor growth modelling:
A methodology for the estimation of the unknown parameters of non-linear Gompertz growth models (commonly used to describe the growth of various systems) has been developed. It's assumed that both process and measurement noise affect the system. Our aim is to compute the system and the noise parameters. The results include a method which is a non-standard exact form of maximum likelihood estimation, where numerical integration is used to approximate the likelihood of the measurements, along with a novel way to reduce the required computations. Synthetic data were first used with promising results. Then, we tested the proposed methods in mice skin tumors of de novo carcinogenesis. Our results show that the maximum likelihood estimator can provide, in most cases, more accurate predictions than the non–linear least squares estimator, which is commonly used in the literature. Moreover, the maximum a posteriori estimator has the potential to correct potentially non-realistic estimates for the carrying capacity at early growth stages.
Furthermore, the project started with a careful literature review which resulted in a very detailed report covering the state of the art and open questions both in smart grids and distributed control. Planning for future projects has been also made.
Additional training and networking activities took place, including the participation of the ER in a course at TU Berlin.
