Safety-Constrained Learning and Control using Scarce Data and Reciprocal Barriers

TL;DR

This paper introduces a novel safety-constrained control algorithm that guarantees system safety using scarce online data and reciprocal barriers, without relying on traditional assumptions about system dynamics.

Contribution

It develops a data-driven control method that overcomes limitations of existing approaches by not requiring global bounds or prior knowledge of unknown dynamics.

Findings

Ensures system safety via forward invariance of the safe set.

Handles controllability loss due to control-direction nullspace.

Operates effectively with limited online data.

Abstract

We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control. It is based on data obtained online from the current trajectory and the concept of reciprocal barriers. More specifically, it first uses the obtained data to calculate set-valued functions that over-approximate the unknown dynamic terms. For the second step of the algorithm, we design a robust control scheme that uses these functions as well as reciprocal barriers to render the system forward invariant with respect to the safe set. In addition, we provide an extension of the algorithm that tackles issues of controllability loss incurred by the nullspace of the control-direction matrix. The algorithm removes a series of standard, limiting assumptions considered in the related literature since it does not require global boundedness, growth conditions, or a priori approximations of the unknown dynamics' terms.