Resilience of Linear Systems to Partial Loss of Control Authority

TL;DR

This paper analyzes the resilience of linear control systems to partial actuator loss, establishing conditions for continued controllability and quantifying performance degradation using Lyapunov bounds, with practical examples.

Contribution

It provides a necessary and sufficient controllability condition for resilient linear systems under actuator loss and derives bounds on their reach times to quantify performance impact.

Findings

Resilience condition for linear systems under partial actuator loss.

Analytical bounds on system reach times during malfunctions.

Validation on aerospace and temperature control systems.

Abstract

After a loss of control authority over thrusters of the Nauka module, the International Space Station lost attitude control for 45 minutes with potentially disastrous consequences. Motivated by this scenario, we investigate the continued capability of control systems to perform their task despite partial loss of authority over their actuators. We say that a system is resilient to such a malfunction if for any undesirable inputs and any target state there exists an admissible control driving the state to the target. Building on controllability conditions and differential games theory, we establish a necessary and sufficient condition for the resilience of linear systems. As their task might be time-constrained, ensuring completion alone is not sufficient. We also want to estimate how much slower the malfunctioning system is compared to its nominal performance. Relying on Lyapunov theory we derive analytical bounds on the reach times of the nominal and malfunctioning systems in order to quantify their resilience. We illustrate our work on the ADMIRE fighter jet model and on a temperature control system.