# Continuous-time control synthesis under nested signal temporal logic specifications

arXiv: https://arxiv.org/abs/2309.14347 · HTML: https://mlsanity.com/paper/2309.14347/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps](https://mlsanity.com/paper/2605.01222/) (2026)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)

## Abstract (arXiv)

In this work, we propose a novel approach for the continuous-time control synthesis of nonlinear systems under nested signal temporal logic (STL) specifications. While the majority of existing literature focuses on control synthesis for STL specifications without nested temporal operators, addressing nested temporal operators poses a notably more challenging scenario and requires new theoretical advancements. Our approach hinges on the concepts of signal temporal logic tree (sTLT) and control barrier function (CBF). Specifically, we detail the construction of an sTLT from a given STL formula and a continuous-time dynamical system, the sTLT semantics (i.e., satisfaction condition), and the equivalence or under-approximation relation between sTLT and STL. Leveraging the fact that the satisfaction condition of an sTLT is essentially keeping the state within certain sets during certain time intervals, it provides explicit guidelines for the CBF design. The resulting controller is obtained through the utilization of an online CBF-based program coupled with an event-triggered scheme for online updating the activation time interval of each CBF, with which the correctness of the system behavior can be established by construction. We demonstrate the efficacy of the proposed method for single-integrator and unicycle models under nested STL formulas.