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Invariant-Based Inverse Engineering for Balanced Displacement of a Cartpole System

Author

Listed:
  • Ion Lizuain

    (Department of Applied Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain
    EHU Quantum Center, University of the Basque Country UPV/EHU, 48940 Leioa, Spain)

  • Ander Tobalina

    (Department of Applied Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain
    EHU Quantum Center, University of the Basque Country UPV/EHU, 48940 Leioa, Spain)

  • Alvaro Rodriguez-Prieto

    (Department of Applied Mathematics, University of the Basque Country UPV/EHU, 48940 Leioa, Spain
    EHU Quantum Center, University of the Basque Country UPV/EHU, 48940 Leioa, Spain)

Abstract

Adiabaticity is a key concept in physics, but its applications in mechanical and control engineering remain underexplored. Adiabatic invariants ensure robust dynamics under slow changes, but they impose impractical time limitations. Shortcuts to Adiabaticity (STA) overcome these limitations by enabling fast operations with minimal final excitations. In this work, we set a STA strategy based on dynamical invariants and inverse engineering to design the trajectory of a cartpole, a system characterized by its instability and repulsive potential. The trajectories found guarantee a balanced transport of the cartpole within the small oscillations regime. The results are compared to numerical simulations with the exact non-linear model to set the working domain of the designed protocol.

Suggested Citation

  • Ion Lizuain & Ander Tobalina & Alvaro Rodriguez-Prieto, 2025. "Invariant-Based Inverse Engineering for Balanced Displacement of a Cartpole System," Mathematics, MDPI, vol. 13(8), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1220-:d:1630231
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