Philip Preußler - MAST

Control in infinite-dimensional systems theory

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EEMCS

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Description:

The project is centered around estimates arising in the study of control systems governed by partial differential equations. For instance, such a setting is given by a simple boundary value problem for a partial differential equation with time dependent Dirichlet boundary data u serving as input and the temperature as state x(t_0) at some fixed time t_0 > 0. One related question is to find sharp parameters p ∈ [1,∞) such that the mapping of u to x(t_0) is well-defined from L^p([0, T]; Γ) → L^2(Ω), where Γ stands for a suitable space of boundary functions on ∂Ω.

 Such space-time estimates are conceptualized within the notion of admissibility in control theory, and they are particularly relevant in the context of control acting via the boundary. Methods to assess these estimates range from classical methods in partial differential equations, over harmonic analysis to operator theory. Another example where such estimates are currently under investigation is within the class of port-Hamiltonian systems, which corresponds to hyperbolic partial differential equations.


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