Computing Safety Margins of Parameterized Nonlinear Systems for Vulnerability Assessment via Trajectory Sensitivities

TL;DR

This paper introduces a new method to compute safety margins for nonlinear systems by analyzing trajectory sensitivities, providing theoretical guarantees and improving vulnerability assessment accuracy.

Contribution

It develops a novel characterization of safety margins using trajectory sensitivities, offering well-posedness and convergence guarantees for the algorithms.

Findings

Algorithms are efficient and non-conservative

Theoretical guarantees ensure algorithm robustness

Successful application to diverse nonlinear systems

Abstract

Physical systems experience nonlinear disturbances which have the potential to disrupt desired behavior. For a particular disturbance, whether or not the system recovers from the disturbance to a desired stable equilibrium point depends on system parameter values, which are typically uncertain and time-varying. Therefore, to quantify proximity to vulnerability we define the safety margin to be the smallest change in parameter values from a nominal value such that the system will no longer be able to recover from the disturbance. Safety margins are valuable but challenging to compute as related methods, such as those for robust region of attraction estimation, are often either overly conservative or computationally intractable for high dimensional systems. Recently, we developed algorithms to compute safety margins efficiently and non-conservatively by exploiting the large sensitivity of the system trajectory near the region of attraction boundary to small perturbations. Although these algorithms have enjoyed empirical success, they lack theoretical guarantees that would ensure their generalizability. This work develops a novel characterization of safety margins in terms of trajectory sensitivities, and uses this to derive well-posedness and convergence guarantees for these algorithms, enabling their generalizability and successful application to a large class of nonlinear systems.