Disturbance Bounds for Signal Temporal Logic Task Satisfaction: A Dynamics Perspective

TL;DR

This paper introduces a method to determine disturbance bounds for Signal Temporal Logic tasks that do not require prior disturbance knowledge, enhancing understanding of controller robustness through a dynamics-based approach.

Contribution

It presents a novel technique to compute disturbance bounds for controllers without prior disturbance information, improving robustness analysis from a control dynamics perspective.

Findings

The disturbance bounds accurately predict system robustness.

Simulation with 1000 trials confirms controllers satisfy specifications within bounds.

The approach does not require prior disturbance knowledge.

Abstract

This letter offers a novel approach to Test and Evaluation of pre-existing controllers from a control barrier function and dynamics perspective. More aptly, prior Test and Evaluation techniques tend to require apriori knowledge of a space of allowable disturbances. Our work, however, determines a two-norm disturbance-bound rejectable by a system's controller without requiring specific knowledge of these disturbances beforehand. The authors posit that determination of such a disturbance bound offers a better understanding of the robustness with which a given controller achieves a specified task - as motivated through a simple, linear-system example. Additionally, we show that our resulting disturbance bound is accurate through simulation of 1000 randomized trials in which a Segway-controller pair satisfies its specification despite randomized perturbations within our identified bound.