Compositional synthesis of almost maximally permissible safety controllers

TL;DR

This paper introduces a decentralized compositional approach for synthesizing safety controllers in interconnected discrete-time linear systems, enabling scalable and effective safety guarantees through local controller design and composition.

Contribution

It presents a novel decentralized synthesis scheme leveraging robust controlled invariant sets for complex interconnected systems, demonstrated on a vehicular platooning example.

Findings

Effective local safety controllers are computed for subsystems.

System-wide safety is guaranteed through controller composition.

Approach reduces complexity of safety controller synthesis.

Abstract

In this work, we present a compositional safety controller synthesis approach for the class of discrete-time linear control systems. Here, we leverage a state-of-the-art result on the computation of robust controlled invariant sets. To tackle the complexity of controller synthesis over complex interconnected systems, this paper introduces a decentralized controller synthesis scheme. Rather than treating the interconnected system as a whole, we first design local safety controllers for each subsystem separately to enforce local safety properties, with polytopic state and input constraints as well as bounded disturbance set. Then, by composing the local controllers, the interconnected system is guaranteed to satisfy the overall safety specification. Finally, we provide a vehicular platooning example to illustrate the effectiveness of the proposed approach by solving the overall safety controller synthesis problem by computing less complex local safety controllers for subsystems and then composing them.