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Peer-reviewedCC BY 4.0Automatica

Optimal Control Under Signal Temporal Logic Constraints: A Robust Reformulation via Augmented Dynamics

  • En Lai
  • Riccardo Bonalli
  • Antoine Girard
  • Frédéric Jean
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Abstract

This work presents a novel approach for solving optimal control problems under Signal Temporal Logic (STL) constraints. The proposed method reformulates the original problem as a classical continuous-time optimal control problem by augmenting the system dynamics with auxiliary variables that encode STL satisfaction through their evolution and boundary conditions. Introducing a robustness parameter, we also establish the convergence of the reformulated problem to the original one as this parameter tends to zero. The proposed method applies to a fragment of STL, which excludes nestings between the until and release operators, but still captures a broad class of STL specifications used in practice. Numerical simulations are realized to demonstrate the feasibility of our method, highlighting its potential for practical applications.

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Cite

BibTeXRIS
BibTeX
@article{lai2026optimal,
  title = {{Optimal Control Under Signal Temporal Logic Constraints: A Robust Reformulation via Augmented Dynamics}},
  author = {En Lai and Riccardo Bonalli and Antoine Girard and Frédéric Jean},
  journal = {Automatica},
  year = {2026},
  month = sep,
  doi = {10.1016/j.automatica.2026.113337},
  url = {https://hal.science/hal-05199224v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Optimal Control Under Signal Temporal Logic Constraints: A Robust Reformulation via Augmented Dynamics
AU  - En Lai
AU  - Riccardo Bonalli
AU  - Antoine Girard
AU  - Frédéric Jean
PY  - 2026
DA  - 2026/09/11
JO  - Automatica
DO  - 10.1016/j.automatica.2026.113337
UR  - https://hal.science/hal-05199224v2
AB  - This work presents a novel approach for solving optimal control problems under Signal Temporal Logic (STL) constraints. The proposed method reformulates the original problem as a classical continuous-time optimal control problem by augmenting the system dynamics with auxiliary variables that encode STL satisfaction through their evolution and boundary conditions. Introducing a robustness parameter, we also establish the convergence of the reformulated problem to the original one as this parameter tends to zero. The proposed method applies to a fragment of STL, which excludes nestings between the until and release operators, but still captures a broad class of STL specifications used in practice. Numerical simulations are realized to demonstrate the feasibility of our method, highlighting its potential for practical applications.
SN  - 0005-1098
ER  -