Synthesizing Safety Controllers for Uncertain Linear Systems: A Direct Data-driven Approach

TL;DR

This paper introduces a direct data-driven method to synthesize safety controllers for unknown linear systems with disturbances, avoiding explicit system identification by using convex optimization on collected data.

Contribution

It proposes a novel $oldsymbol{ ext{ extgamma}}$-robust safety invariant framework and formulates data-driven synthesis as convex optimization problems with LMIs, applicable from a single trajectory.

Findings

Successfully applied to a 4D inverted pendulum system.

Demonstrates effectiveness without explicit system identification.

Provides a scalable approach for safety control synthesis.

Abstract

In this paper, we provide a direct data-driven approach to synthesize safety controllers for unknown linear systems affected by unknown-but-bounded disturbances, in which identifying the unknown model is not required. First, we propose a notion of $\gamma$-robust safety invariant ($\gamma$-RSI) sets and their associated state-feedback controllers, which can be applied to enforce invariance properties. Then, we formulate a data-driven computation of these sets in terms of convex optimization problems with linear matrix inequalities (LMI) as constraints, which can be solved based on a finite number of data collected from a single input-state trajectory of the system. To show the effectiveness of the proposed approach, we apply our results to a 4-dimensional inverted pendulum.