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

系统和控制理论的研究领域是工程科学的重要组成部分，在许多学科中具有实际意义，从可持续制造，社会数字化到自动驾驶汽车。传统上，控制器是根据数学模型推导出来的，并且可以严格保证其正常和安全的功能。目前在各个领域利用数据，特别是学习技术的趋势也强烈影响着自动控制领域。有人建议，而不是数学上严格的基于模型的方法，学习控制器使用的主要优点是一个更简单，更便宜，可能更通用的应用程序。然而，这带来的缺点是，在大多数情况下，不能保证闭环的安全和可靠的操作。在拟议的Koselleck项目中，我们打算开发一种新的基于数据的控制理论，该理论将允许在不需要数学系统模型的情况下赋予控制回路以系统理论保证。为此，我们计划研究如何系统地利用数据中包含的可用信息，以便仅基于测量数据来描述、分析和控制系统。虽然目前在这个方向上的第一步是为满足叠加原理的线性系统，本项目的目标是为一般非线性系统开发一个框架。这是向前迈出的重要但极具挑战性的一步，需要对问题有全新的看法，但作为回报，它的实际相关性大大增加。作为第二个目标，这个新的框架应该不仅允许单独使用数据，而且还允许使用任何（可能是部分）可用的模型知识。这将允许在一般的混合设置中利用两个世界中的最佳。

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.