# Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method

## TL;DR

This paper introduces a symbolic control synthesis approach for nonlinear sampled switched systems using Euler's method, providing guaranteed control with bounded error, and compares it with Runge-Kutta based methods.

## Contribution

It presents a novel control synthesis method leveraging Euler's method for nonlinear systems with bounded error guarantees, implemented in Octave.

## Key findings

- The Euler-based method achieves comparable results to Runge-Kutta methods.
- Bounded error is ensured through appropriate discretization.
- Implementation in Octave demonstrates practical applicability.

## Abstract

In this paper, we propose a symbolic control synthesis method for nonlinear sampled switched systems whose vector fields are one-sided Lipschitz. The main idea is to use an approximate model obtained from the forward Euler method to build a guaranteed control. The benefit of this method is that the error introduced by symbolic modeling is bounded by choosing suitable time and space discretizations. The method is implemented in the interpreted language Octave. Several examples of the literature are performed and the results are compared with results obtained with a previous method based on the Runge-Kutta integration method.