# Formal Synthesis of Control Strategies for Positive Monotone Systems

arXiv: https://arxiv.org/abs/1702.08501 · HTML: https://mlsanity.com/paper/1702.08501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2017.

## Built on by (most cited first, 1 of 1)

- [Distributed Identification of Contracting and/or Monotone Network Dynamics](https://mlsanity.com/paper/2107.14309/) (2021)

## Abstract (arXiv)

We design controllers from formal specifications for positive discrete-time monotone systems that are subject to bounded disturbances. Such systems are widely used to model the dynamics of transportation and biological networks. The specifications are described using signal temporal logic (STL), which can express a broad range of temporal properties. We formulate the problem as a mixed-integer linear program (MILP) and show that under the assumptions made in this paper, which are not restrictive for traffic applications, the existence of open-loop control policies is sufficient and almost necessary to ensure the satisfaction of STL formulas. We establish a relation between satisfaction of STL formulas in infinite time and set-invariance theories and provide an efficient method to compute robust control invariant sets in high dimensions. We also develop a robust model predictive framework to plan controls optimally while ensuring the satisfaction of the specification. Illustrative examples and a traffic management case study are included.