# Backward Reachability for Polynomial Systems on A Finite Horizon

arXiv: https://arxiv.org/abs/1907.03225 · HTML: https://mlsanity.com/paper/1907.03225/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Unifying Hamilton-Jacobi Reachability and Reinforcement Learning](https://mlsanity.com/paper/2601.08050/) (2026)

## Abstract (arXiv)

A method is presented to obtain an inner-approximation of the backward reachable set (BRS) of a given target tube, along with an admissible controller that maintains trajectories inside this tube. The proposed optimization algorithms are formulated as nonlinear optimization problems, which are decoupled into tractable subproblems and solved by an iterative algorithm using the polynomial S-procedure and sum-of-squares techniques. This framework is also extended to uncertain nonlinear systems with L2 disturbances and L∞ parametric uncertainties. The effectiveness of the method is demonstrated on several nonlinear robotics and aircraft systems with control saturation.