Flatness of Semilinear Parabolic PDEs—A Generalized Cauchy–Kowalevski Approach

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.