Energetic Resilience of Linear Driftless Systems

TL;DR

This paper introduces an energetic resilience metric for linear driftless systems to quantify the maximum additional energy required during malfunctions that disable some actuators, with derivations and a simulation example.

Contribution

It develops a new metric and analytical bounds for energetic resilience in linear systems under actuator malfunctions, including special cases and practical implications.

Findings

Derived optimal control signals and minimum energies for nominal and malfunctioning systems.

Established bounds on worst-case energy increase due to malfunctions.

Demonstrated the metric's usefulness with a simulation on an underwater robot model.

Abstract

When a malfunction causes a control system to lose authority over a subset of its actuators, achieving a task may require spending additional energy in order to compensate for the effect of uncontrolled inputs. To understand this increase in energy, we introduce an energetic resilience metric that quantifies the maximal additional energy required to achieve finite-time regulation in linear driftless systems that suffer this malfunction. We first derive optimal control signals and minimum energies to achieve this task in both the nominal and malfunctioning systems. We then obtain a bound on the worst-case energy used by the malfunctioning system, and its exact expression in the special case of loss of authority over one actuator. Further considering this special case, we derive a bound on the metric for energetic resilience. A simulation example on a model of an underwater robot demonstrates that this bound is useful in quantifying the increased energy used by a system suffering such a malfunction.