Control of distributed-parameter systems using normal forms

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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.