Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Motion Planning for PDEs

  • Thomas Meurer
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_14


Motion planning refers to the design of an open-loop or feedforward control to realize prescribed desired paths for the system states or outputs. For distributed-parameter systems described by partial differential equations (PDEs), this requires to take into account the spatial-temporal system dynamics. Here, flatness-based techniques provide a systematic inversion-based motion planning approach, which is based on the parametrization of any system variable by means of a flat or basic output. With this, the motion planning problem can be solved rather intuitively as is illustrated for linear and semilinear PDEs.


Basic output Flatness Formal integration Formal power series Trajectory assignment Trajectory planning Transition path 
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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Thomas Meurer
    • 1
  1. 1.Faculty of EngineeringChristian-Albrechts-University KielKielGermany