Safe Controlled Invariance for Linear Systems Using Sum-of-Squares Programming

TL;DR

This paper presents a straightforward sum-of-squares programming approach to synthesize safe invariant sets and controllers for linear systems, ensuring safety guarantees.

Contribution

It introduces a novel invariance-based method that simplifies the synthesis of safe controllers for linear systems using sum-of-squares programming.

Findings

Provides a new method for safe invariant set synthesis

Ensures safety guarantees for linear systems

Simplifies the controller synthesis process

Abstract

Safety is closely related to set invariance for dynamical systems. However, synthesizing a safe invariant set and at the same time synthesizing the associated safe controller still remains challenging. In this note we introduce a simple invariance-based method for linear systems with safety guarantee. The proposed method uses sum-of-squares programming.