# Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

## TL;DR

This paper introduces Piecewise Robust Barrier Tubes, an efficient method for overapproximating nonlinear hybrid systems with uncertainty, improving soundness and precision over existing approaches.

## Contribution

It extends PBT to handle hybrid systems with uncertainty and significantly improves computational efficiency by avoiding interval methods.

## Key findings

- More efficient than existing methods
- More precise overapproximations
- Successfully evaluated on benchmarks

## Abstract

Piecewise Barrier Tubes (PBT) is a new technique for flowpipe overapproximation for nonlinear systems with polynomial dynamics, which leverages a combination of barrier certificates. PBT has advantages over traditional time-step based methods in dealing with those nonlinear dynamical systems in which there is a large difference in speed between trajectories, producing an overapproximation that is time independent. However, the existing approach for PBT is not efficient due to the application of interval methods for enclosure-box computation, and it can only deal with continuous dynamical systems without uncertainty. In this paper, we extend the approach with the ability to handle both continuous and hybrid dynamical systems with uncertainty that can reside in parameters and/or noise. We also improve the efficiency of the method significantly, by avoiding the use of interval-based methods for the enclosure-box computation without loosing soundness. We have developed a C++ prototype implementing the proposed approach and we evaluate it on several benchmarks. The experiments show that our approach is more efficient and precise than other methods in the literature.