Linear model predictive safety certification for learning-based control

TL;DR

This paper introduces a model predictive safety certification scheme for linear systems with learning-based controllers, ensuring safety constraints are met despite model uncertainties, and provides a practical data-driven design method.

Contribution

It proposes a novel MPC-based safety certification method that verifies and minimally modifies learning inputs to maintain safety in uncertain linear systems.

Findings

Ensures safety constraints under model uncertainty.

Provides an iterative method to enlarge the safe set.

Offers a data-driven scenario optimization design procedure.

Abstract

While it has been repeatedly shown that learning-based controllers can provide superior performance, they often lack of safety guarantees. This paper aims at addressing this problem by introducing a model predictive safety certification (MPSC) scheme for polytopic linear systems with additive disturbances. The scheme verifies safety of a proposed learning-based input and modifies it as little as necessary in order to keep the system within a given set of constraints. Safety is thereby related to the existence of a model predictive controller (MPC) providing a feasible trajectory towards a safe target set. A robust MPC formulation accounts for the fact that the model is generally uncertain in the context of learning, which allows proving constraint satisfaction at all times under the proposed MPSC strategy. The MPSC scheme can be used in order to expand any potentially conservative set of safe states for learning and we prove an iterative technique for enlarging the safe set. Finally, a practical data-based design procedure for MPSC is proposed using scenario optimization.