Distributed Model Predictive Safety Certification for Learning-based Control

TL;DR

This paper introduces a distributed safety certification framework for learning-based control of large-scale systems, ensuring safety constraints are met while improving control performance through a novel distributed tube-based MPC approach.

Contribution

It extends centralized safety certification methods to a distributed setting, enabling safe learning-based control with local negotiations and invariant tubes in uncertain systems.

Findings

Guarantees constraint satisfaction for unsafe policies

Improves control performance over robust distributed MPC

Demonstrates effectiveness through numerical simulations

Abstract

While distributed algorithms provide advantages for the control of complex large-scale systems by requiring a lower local computational load and less local memory, it is a challenging task to design high-performance distributed control policies. Learning-based control algorithms offer promising opportunities to address this challenge, but generally cannot guarantee safety in terms of state and input constraint satisfaction. A recently proposed safety framework for centralized linear systems ensures safety by matching the learning-based input online with the initial input of a model predictive control law capable of driving the system to a terminal set known to be safe. We extend this idea to derive a distributed model predictive safety certification (DMPSC) scheme, which is able to ensure state and input constraint satisfaction when applying any learning-based control algorithm to an uncertain distributed linear system with dynamic couplings. The scheme is based on a distributed tube-based model predictive control (MPC) concept, where subsystems negotiate local tube sizes among neighbors in order to mitigate restrictiveness of the safety approach. In addition, we present a technique for generating a structured ellipsoidal robust positive invariant tube. In numerical simulations, we show that the safety framework ensures constraint satisfaction for an initially unsafe control policy and allows to improve overall control performance compared to robust distributed MPC.