B. Schörkhuber, T. Meurer, A. Jüngel:
"Flatness of Semilinear Parabolic PDEs - A Generalized Cauchy-Kowalevski Approach";
IEEE Transactions on Automatic Control, 58 (2013), 9; S. 2277 - 2291.

Kurzfassung deutsch:
Siehe englisches Abstract.

Kurzfassung englisch:
A generalized Cauchy-Kowalevski approach is
proposed for flatness-based trajectory planning for boundary controlled
semilinear systems of partial differential equations (PDEs)
in a one-dimensional spatial domain. For this, the ansatz presented
in "Trajectory planning for boundary controlled parabolic PDEs
with varying parameters on higher-dimensional spatial domains"
(T. Meurer and A. Kugi, IEEE Trans. Autom. Control, vol. 54, no,
8, pp. 1854-1868, Aug. 2009) using formal integration is generalized
towards a unified design framework, which covers linear and
semilinear PDEs including rather broad classes of nonlinearities
arising in applications. In addition, an efficient semi-numerical
solution of the implicit state and input parametrizations is developed
and evaluated in different scenarios. Simulation results
for various types of nonlinearities and a tubular reactor model
described by a system of semilinear reaction-diffusion-convection
equations illustrate the applicability of the proposed method.

Nonlinear control systems; trajectory planning

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