# Control of Multi-Agent Systems with Finite Time Control Barrier Certificates and Temporal Logic

arXiv: https://arxiv.org/abs/1808.02393 · HTML: https://mlsanity.com/paper/1808.02393/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2018.

## Built on by (most cited first, 6 of 6)

- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [Safe multi-agent motion planning under uncertainty for drones using filtered reinforcement learning](https://mlsanity.com/paper/2311.00063/) (2023)
- [Distributed Mission Planning of Complex Tasks for Heterogeneous Multi-Robot Teams](https://mlsanity.com/paper/2109.10106/) (2021)
- [Robust Taylor-Lagrange Control for Safety-Critical Systems](https://mlsanity.com/paper/2602.20076/) (2026)

## Abstract (arXiv)

In this paper, a method to synthesize controllers using finite time convergence control barrier functions guided by linear temporal logic specifications for continuous time multi-agent dynamical systems is proposed. Finite time convergence to a desired set in the state space is guaranteed under the existence of a suitable finite time convergence control barrier function. In addition, these barrier functions also guarantee forward invariance once the system converges to the desired set. This allows us to formulate a theoretical framework which synthesizes controllers for the multi-agent system. These properties also enable us to solve the reachability problem in continuous time by formulating a theorem on the composition of multiple finite time convergence control barrier functions. This approach is more flexible than existing methods and also allows for a greater set of feasible control laws. Linear temporal logic is used to specify complex task specifications that need to be satisfied by the multi-agent system. With this solution methodology, a control law is synthesized that satisfies the given temporal logic task specification. Robotic experiments are provided which were performed on the Robotarium multi-robot testbed at Georgia Tech.