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Optimal Distributed Control and Application to Smart Grids

Periodic Reporting for period 1 - ODICON-ASMA (Optimal Distributed Control and Application to Smart Grids)

Reporting period: 2017-09-01 to 2019-08-31

This project aimed to produce theoretical results in the control of complex systems as well as to provide control techniques for smart grids, aspiring to be a fruitful interaction between theory and practice, although the applicability of the theoretical developments is not meant to be limited in smart grids.

For a number of reasons the three following specific topics in these two areas of interest were identified as topics of priority:
1. Battery management systems
2. Decentralized control of autonomous vehicles
3. Identification of parameters of non-linear stochastic systems from noisy data
Concerning the third topic, the techniques developed were applied to tumor growth modelling.

These topics are related to societal needs and connections with industry are foreseeable. Smart grid technologies will be definitely deployed in future grids with a high renewable energy penetration so they are important for reducing both the use of nuclear power and carbon dioxide emissions. Therefore, they are related to climate change and the environment. The parts related to cancer and autonomous vehicles are also related to societal challenges recognized in Horizon 2020, health and smart transport respectively. Parameter identification techniques can be applied to a vast variety of systems.

By training through research, the project aimed to support a promising young researcher so that he can move to an internationally active group and develop various skills. Bidirectional transfer of knowledge was also an objective of the project. It should be emphasized that the expertise of the Experienced Researcher (ER) and of the people of the host group is complementary and this combined background forms an excellent basis for this research.
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.
The obtained results constitute a progress beyond the state of the art: In some cases, this project was the first work to provide solutions leading to the optimization of the specific objective criteria, which are important. In other cases, optimizing these criteria is done with a computational efficiency improvement, in comparison to pre-existing techniques.

As this was a basic research project, potential users are, to a large degree, other researchers. Discussions about extensions of the established results have been had with a large number of researchers from various institutions and of various experience levels. However, some contact with people interested in the application of the proposed techniques (rather than in the techniques themselves) has been already made.

All post-prints are made available in open access. To maximize impact, open access to data is also provided on the publisher's site when meaningful, while in other cases, code will be made freely available.

Concerning policy making, the work related to grids can serve as a basis for follow-up work that could influence future regulations about grids with a large penetration of renewable sources and storage. Some of the problems of autonomous vehicles that have been studied involve interaction of the vehicles with suitable infrastructure. Future infrastructure for intelligent transport will need to implement specific standards. Studying problems similar to those of this project can help specify optimal policies.

The fellowship has an important effect on the career of the ER. For two years he had the opportunity to focus on his research in an environment of his choice. Additionally, having been an MSCA fellow is perceived as an important academic credential. Finally, the bidirectional knowledge transfer was beneficial both for the ER and the hosting group. The stay in the hosting group was also helpful in terms of networking.