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

系统与控制理论的研究领域是工程科学的重要组成部分，在从可持续制造、社会数字化到自动驾驶汽车等许多学科中都具有实用意义。传统上，控制器是在数学模型的基础上推导出来的，以这种方式可以为其正确和安全的运行提供严格的保证。目前在各个领域利用数据，特别是学习技术的趋势也对自动控制领域产生了强烈的影响。建议使用学习控制器，而不是数学上严格的基于模型的方法，其主要优点是应用更简单、更便宜，而且可能更通用。然而，这伴随着一个缺点，即在大多数情况下，不能保证闭合回路的安全可靠运行。在建议的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为控制回路提供系统理论保证。为此，我们计划调查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。虽然目前在这一方向上的第一步是对满足叠加原理的线性系统进行的，但这个项目的目标是为一般的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，需要对问题有一个全新的看法，但作为回报，它的实际相关性要大得多。作为第二个目标，理想情况下，这个新框架不仅应该允许单独使用数据，还应该允许使用可能可用的任何(可能是部分)模型知识。这将允许在一般的混合环境中利用这两个世界的最好之处。

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.