# Synthesizing communication plans for reachability and safety specifications

## TL;DR

This paper develops control and communication strategies for nonlinear networked control systems to ensure reachability of a target set and safety constraints, using Lyapunov functions and abstraction methods.

## Contribution

It introduces a novel approach combining $elta$-ISS control Lyapunov functions with abstraction schemes for efficient communication scheduling.

## Key findings

- Effective control and communication strategies validated by simulations.
- Guarantees of reachability and safety under the proposed schemes.
- Reduced computational complexity through abstraction and graph search.

## Abstract

We propose control and communication strategies for nonlinear networked control systems subject to state and input constraints. The objective is to steer the state of the system towards a prescribed target set in finite time (\textit{reachability}), while at the same time remaining inside a safety set for all time (\textit{safety}). By leveraging the notion of $\delta$-ISS control Lyapunov function, we derive a sufficient condition to generate a communication scheduling, such that the resulting state trajectory guarantees reachability and safety. Moreover, in order to alleviate computational burden we present a way to find a suitable communication scheduling by implementing abstraction schemes and standard graph search methodologies. Simulation examples validate the effectiveness of the proposed approach.