This master thesis deals with trajectory planning for linear diffusion-convection-reaction systems. Exploiting the properties of so called Riesz spectral operators, a spectral representation of the system is developed. Proceeding from the spectral representation, a flatness-based parametrization of the states and inputs by basic outputs is systematically derived. Since infinite products in the Laplace variable or respectively differential operators of infinite order are involved in the parametrization, meaningful results require convergence of the regarding terms. To enhance the convergence behavior of these terms, so called Weierstrass canonical products are introduced.
Furthermore a convergence analysis is performed, which utilizes the theory of entire functions and imposes certain demands on feasible basic outputs. Based on the system parametrization, trajectories for the basic outputs are specified, which ensure a desired behavior for the output trajectories. In this thesis, transitions between stationary profiles of the outputs and the decoupled assignment of more general output trajectories are considered. These concepts are realized seminumerically, including the application of an appropriate discretization method and a modal reduction of the system. Finally, simulation results are presented to illustrate the trajectory planning concepts.