A new unitary control theory for nonlinear systems: Merging models and data

点击翻译按钮获取中文摘要

The research field of systems and control theory is an important part of engineering science with practical relevance in many disciplines ranging from sustainable manufacturing, digitalization of society to autonomous vehicles. Classically, controllers are derived on the basis of mathematical models and in such a way that rigorous guarantees can be given for their proper and safe functioning. The current trends to utilize data and especially learning techniques in various fields are also strongly influencing the automatic control field. It is suggested that instead of mathematically rigorous model-based approaches, learned controllers are used with the main advantage of a simpler, cheaper, and possibly more versatile application. However, this comes with the drawback that in most cases no guarantees for a safe and reliable operation of the closed loop can be given. In the proposed Koselleck project, we intend to develop a new data-based control theory that will allow to endow control loops with systems theoretic guarantees without the need for mathematical system models. To this end, we plan to investigate how available information contained in the data can be systematically exploited in order to describe, analyze, and control systems based only on measured data. While first steps in that direction are currently undertaken for linear systems satisfying the superposition principle, the goal of this project is to develop a framework for general nonlinear systems. This is an important but very challenging step forward that requires a completely new view on the problem, but comes with a much increased practical relevance as reward. As a second goal, this new framework should ideally allow to not only use data alone, but also any (possibly partial) model knowledge that may be available. This will allow to exploit the best of the two worlds in a general hybrid setting.