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Quantitative Resilience of Linear Driftless Systems.

Jean-Baptiste Bouvier¹, Kathleen Xu¹, Melkior Ornik²

¹Department of Aerospace Engineering, University of Illinois at Urbana-Champaign. Urbana, IL 61801, USA.

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Summary

This summary is machine-generated.

This study introduces quantitative resilience for control systems, measuring performance loss after actuator failure. An efficient method is presented to calculate this metric, reducing complex computations to a single optimization problem.

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Area of Science:

Control Systems Engineering
System Dynamics

Background:

Control systems can lose actuator authority, leading to performance degradation.
Resilience ensures systems reach targets despite malfunctions, but speed may decrease.

Purpose of the Study:

Introduce and quantify system performance loss after control authority failure.
Develop an efficient computational method for quantitative resilience.

Main Methods:

Define quantitative resilience as the ratio of minimal reachability times (initial vs. malfunctioning).
Utilize control theory and novel geometric results.
Reduce complex nested optimization to a single linear optimization problem.

Main Results:

An efficient method for computing quantitative resilience is established.
The computation is simplified from nested nonlinear optimizations to a linear optimization problem.
The method's efficacy is demonstrated using an opinion dynamics model.

Conclusions:

The proposed method efficiently calculates quantitative resilience.
This work provides a valuable metric for assessing system robustness under actuator failure.
The findings are applicable to various control system scenarios, including opinion dynamics.