Control of distributed-parameter systems using normal forms

基于项目合作伙伴在分布参数系统分析、控制和观测领域的成功共同研究，发展了线性和非线性系统的统一规范形方法。重点介绍了当前这类系统控制理论的两个主要研究方向，即所谓的反推方法和基于平坦度的方法。这些方法被推广到大类相互关联的系统，这些系统可能是双曲型和抛物型的，并且涉及线性或非线性边界动力学，其中欠驱动和部分传感起着突出的作用。然后，这些系统被用作可灵活配置的大规模互连的构建块。所研究的设计与所谓的控制器和观测器范式密切相关，而且有助于分析可控性和能观性。因此，这些范式的推广，它们的详细分析，以及相关等价问题的研究，是该项目的中心和统一部分。严格反馈和严格前馈形式的刻画是另一个重要的问题。与这些调查相辅相成的是基于解决方案的方法的发展，这些方法作为既定方法之间的统一纽带，其中隐含地使用基于解决方案的预测。因此，该项目的成果将是一个新的通用范式框架，用于基于观测器的跟踪控制和大类系统的输出调节。它补充并在很大程度上推广了现有的结果，同时也统一了它们，并在分布参数系统的控制理论中开辟了新的研究途径。

Building on successful common research of the project partners in the field of analysis, control, and observation of distributed-parameter systems, a unified normal form approach is developed for linear and classes of nonlinear systems. The focus is on two major current research directions in the control theory for these classes of systems, the so-called backstepping and flatness-based approaches. These methods are generalized to large classes of interconnected systems that may be of hyperbolic and parabolic type and involve linear or nonlinear boundary dynamics, where underactuation and partial sensing play a prominent role. These systems are then used as building blocks in flexibly configurable large-scale interconnections. Investigated designs are intimately related to so-called controller and observer normal forms that, moreover, facilitate the analysis of controllability and observability properties. Generalization of these normal forms, their detailed analysis, and the study of the related equivalence problems is, thus, a central and unifying part of the project. Characterization of strict-feedback and strict-feedforward forms is another important issue. These investigations are complemented by the development of solution-based methods that serve as a unifying link between the established approaches, where solution-based predictions are implicitly used. The outcome of this project will, thus, be a new general normal form framework for observer-based tracking control and output regulation for large classes of systems. It complements and largely generalizes existing results, while also unifying them, and it opens new research avenues in the control theory for distributed-parameter systems.