# Cause Mining and Controller Synthesis with STL

## TL;DR

This paper introduces a novel method for controlling cyber-physical systems by identifying causes of unwanted events using STL and synthesizing controllers to minimize these events, applicable to systems with finite control options.

## Contribution

It presents an alternative cause-based approach for controller synthesis using STL, addressing limitations of formal methods in complex or stochastic systems.

## Key findings

- Reduces the number of unwanted events in system traces
- Applicable to systems with finitely many control choices
- Validated on traffic congestion avoidance example

## Abstract

Formal control of cyber-physical systems allows for synthesis of control strategies from rich specifications such as temporal logics. However, the classes of systems that the formal approaches can be applied to is limited due to the computational complexity. Furthermore, the synthesis problem becomes even harder when non-determinism or stochasticity is considered. In this work, we propose an alternative approach. First, we mark the unwanted events on the traces of the system and generate a controllable cause representing these events as a Signal Temporal Logic (STL) formula. Then, we synthesize a controller based on this formula to avoid the satisfaction of it. Our approach is applicable to any system with finitely many control choices. While we can not guarantee correctness, i.e., the unwanted events will never occur, we show on an example that the proposed approach reduces the number of the unwanted events. In particular, we validate it for the congestion avoidance problem in a traffic network.