A unified normal form approach is developed for linear and nonlinear distributed-parameter systems (DPSs). To this end, two major current research directions in the control theory for DPSs, the backstepping and the flatness-based approach, are extended to new classes of DPSs. Their mutual relationships are investigated to obtain new general and coherent analysis and synthesis methods. Classes considered comprise hyperbolic and parabolic PDEs with boundary dynamics as well as interconnected partial differential equations (PDEs). Starting from linear systems with linear lumped boundary dynamics, the project successively extends the methods to semilinear and quasilinear PDEs with nonlinear dynamics at the boundaries. Special emphasis is put on coupled PDEs of both hyperbolic and parabolic type and on underactuated systems. These systems are used as building blocks in general interconnections, thus covering more complex dynamical systems, for which new efficient methods are developed to reach a decentralized design. The interconnection of these methods with the normal form approach is shown below.

The focus at JKU is on flatness-based and backstepping-based methods for linear DPSs. For an introduction intro the backstepping and the flatness-based approach for so-called PDE-ODE systems as they arise for hyperbolic PDEs with dynamics boundary conditions, e.g. a heavy rope with a load, see the paper "Control of distributed-parameter systems using normal forms: an introduction", opens an external URL in a new window (at - Automatisierungstechnik, 2023).