Pseudo-differential operators in parametrization of boundary-value control systems

Here we present a new approach for the design of open-loop control or motion planning for partial differential equations (PDE) and systems. It is based on pseudo-differential operator (ψDO) theory and applies directly to linear boundary-controlled PDE systems. The key idea is to parametrize the system variables by some external parameters (functions) as it is the case in flatness-based design for ordinary differential equation (ODE) systems. The ψDO theory allows us to invert the PDE operators considered in the same ψDO class where the system models are. This gives a solid basis for the analysis and allows us to connect separate PDE systems like ODE models. Calculated examples illustrate these ideas.