Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version

TL;DR

This paper introduces an adaptive Model Predictive Safety Certification framework for linear systems with uncertainties, enhancing safety and performance through set-membership estimation and iterative safe set enlargement.

Contribution

It develops an adaptive mechanism that improves safety certification by updating the system model and enlarging safe sets, addressing conservativeness in short horizon MPC.

Findings

Safety performance improves with model and safe set adaptation.

The method guarantees recursive feasibility and non-decreasing safety.

Numerical examples demonstrate effectiveness in high-dimensional systems.

Abstract

We propose an adaptive Model Predictive Safety Certification (MPSC) scheme for learning-based control of linear systems with bounded disturbances and uncertain parameters where the true parameters are contained within an a priori known set of parameters. An MPSC is a modular framework which can be used in combination with any learning-based controller to ensure state and input constraint satisfaction of a dynamical system by solving an online optimisation problem. By continuously connecting the current system state with a safe terminal set using a robust tube, safety can be ensured. Thereby, the main sources of conservative safety interventions are model uncertainties and short planning horizons. We develop an adaptive mechanism to improve the system model, which leverages set-membership estimation to guarantee recursively feasible and non-decreasing safety performance improvements. In order to accommodate short prediction horizons, iterative safe set enlargements using previously computed robust backup plans are proposed. Finally, we illustrate the increase of the safety performance through the parameter and safe set adaptation for numerical examples with up to 16 state dimensions.