Flatness of a class of linear Volterra partial integro–differential equations

Flatness–based trajectory planning is addressed for a parabolic–like linear Volterra partial integro–differential equation (PIDE) with boundary control. For this purpose the PIDE is formally integrated which results in an implicit state and input parametrization. Successive approximation is used to explicitly resolve the implicit result in terms of a recursion scheme. Absolute and uniform convergence is verified by restricting the flat output trajectory to Gevrey class functions of a particular order. Simulation results confirm the applicability and illustrate the tracking behavior for finite time transitions between operating points along predefined transition paths.