A Statistical Theory for the Analysis of Uncertain Systems

TL;DR

This paper introduces a new probabilistic robustness measure and sampling strategy that reduce conservativeness and computational complexity in analyzing uncertain systems, enabling efficient hierarchical algorithms.

Contribution

It proposes a less conservative robustness measure and an efficient sampling strategy with algorithms that significantly lower computational complexity.

Findings

The new robustness measure is less conservative than existing ones.

Hierarchical sample reuse algorithms reduce computational complexity.

A simple algorithm relates the new and existing robustness measures.

Abstract

This paper addresses the issues of conservativeness and computational complexity of probabilistic robustness analysis. We solve both issues by defining a new sampling strategy and robustness measure. The new measure is shown to be much less conservative than the existing one. The new sampling strategy enables the definition of efficient hierarchical sample reuse algorithms that reduce significantly the computational complexity and make it independent of the dimension of the uncertainty space. Moreover, we show that there exists a one to one correspondence between the new and the existing robustness measures and provide a computationally simple algorithm to derive one from the other.