# Backward Reachability using Integral Quadratic Constraints for Uncertain Nonlinear Systems

arXiv: https://arxiv.org/abs/2003.05617 · HTML: https://mlsanity.com/paper/2003.05617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentials](https://mlsanity.com/paper/2609.28364/) (2026)

## Abstract (arXiv)

A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives trajectories starting in these sets to the target set. The method merges dissipation inequalities and integral quadratic constraints (IQCs) with both hard and soft IQC factorizations. Computational algorithms are presented using the generalized S-procedure and sum-of-squares techniques. The use of IQCs in backward reachability analysis allows for a variety of perturbations including parametric uncertainty, unmodeled dynamics, nonlinearities, and uncertain time delays. The method is demonstrated on two examples, including a 6-state quadrotor with actuator uncertainties.