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 PDEs in a one-dimensional spatial domain. For this, the ansatz presented in [16] 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 simulation 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.