Approximate Energetic Resilience of Nonlinear Systems under Partial Loss of Control Authority

TL;DR

This paper introduces an energetic resilience metric to quantify how much additional energy nonlinear systems require under partial control loss, providing bounds and approximations validated through simulations.

Contribution

It develops a novel framework for measuring energetic resilience in nonlinear systems with partial control loss, extending prior linear-focused work.

Findings

The metric effectively quantifies resilience without significant conservatism.

Bounds on the resilience metric are derived for systems with one actuator loss.

Simulation results validate the usefulness of the metric in nonlinear contexts.

Abstract

In this paper, we quantify the resilience of nonlinear dynamical systems by studying the increased energy used by all inputs of a system that suffers a partial loss of control authority, either through actuator malfunctions or through adversarial attacks. To quantify the maximal increase in energy, we introduce the notion of an energetic resilience metric. Prior work in this particular setting does not consider general nonlinear dynamical systems. In developing this framework, we first consider the special case of linear driftless systems and recall the energies in the control signal in the nominal and malfunctioning systems. Using these energies, we derive a bound on the energetic resilience metric. For general nonlinear systems, we first obtain a condition on the mean value of the control signal in both the nominal and malfunctioning systems, which allows us to approximate the energy in the control. We then obtain a worst-case approximation of this energy for the malfunctioning system, over all malfunctioning inputs. Assuming this approximation is exact, we derive bounds on the energetic resilience metric when control authority is lost over one actuator. A set of simulation examples demonstrate that the metric is useful in quantifying the resilience of the system without significant conservatism, despite the approximations used in obtaining control energies for nonlinear systems.