Flatness-based trajectory planning for semilinear parabolic PDEs

Trajectory planning is considered for semilinear parabolic partial differential equations (PDEs) with boundary control. For this, a novel flatness-based technique is proposed, which is based on the reformulation of the boundary control problem as a Cauchy problem followed by a formal integration. Solution existence is analyzed using a generalized Cauchy-Kowalevskaja Theorem in suitable Gevrey classes and formal integration. This moreover enables to deduce efficient semi-numerical design techniques, which are illustrated in a simulation scenario.