Control of distributed-parameter systems using normal forms

基于项目合作伙伴在分布参数系统的分析、控制和观测领域的成功共同研究，为线性和非线性系统开发了统一的规范形式方法。重点是两个主要的当前研究方向在控制理论为这些类别的系统，所谓的backstepping和flatness-based方法。这些方法被推广到大类的互联系统，可能是双曲型和抛物型，涉及线性或非线性边界动态，欠驱动和部分传感发挥了突出的作用。然后，这些系统被用作可灵活配置的大规模互连的构建模块。调查设计密切相关的所谓的控制器和观察器的正常形式，而且，便于分析的可控性和可观测性。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特征是另一个重要问题。这些调查是补充的解决方案为基础的方法，作为一个统一的链接之间建立的方法，其中解决方案为基础的预测是隐含使用的发展。因此，该项目的成果将是一个新的通用范式框架，用于大类系统的基于卷积器的跟踪控制和输出调节。它补充并在很大程度上概括了现有的结果，同时也统一了它们，它开辟了新的研究途径，在控制理论的分布参数系统。

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.