# Scalable Safety-Preserving Robust Control Synthesis for Continuous-Time Linear Systems

arXiv: https://arxiv.org/abs/1312.3399 · HTML: https://mlsanity.com/paper/1312.3399/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2013.

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

- [Excluding the Irrelevant: Focusing Reinforcement Learning through Continuous Action Masking](https://mlsanity.com/paper/2406.03704/) (2024)

## Abstract (arXiv)

We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative approximation of the discriminating kernel using robust maximal reachable sets---an extension of our earlier work on computation of the viability kernel for high-dimensional systems. Based on ellipsoidal techniques for reachability, a piecewise ellipsoidal algorithm with polynomial complexity is described that under-approximates the discriminating kernel under LTI dynamics. This precomputed piecewise ellipsoidal set is then used online to synthesize a permissive state-feedback safety-preserving controller. The controller is modeled as a hybrid automaton and can be formulated such that under certain conditions the resulting control signal is continuous across its transitions. We show the performance of the controller on a twelve-dimensional flight envelope protection problem for a quadrotor with actuation saturation and unknown wind disturbances.