Energetic Resilience under Temporal Logic Specifications

TL;DR

This paper introduces an energetic resilience metric for control systems under temporal logic specifications, enabling quantification and synthesis of control inputs resilient to uncertainties and adversarial influences.

Contribution

It proposes a new energetic resilience metric, proves its compositional properties, and provides efficient quadratic program-based synthesis methods for complex specifications.

Findings

The metric quantifies maximum additional energy under undesired effects.

Control synthesis reduces to quadratic programs for certain specifications.

Case studies demonstrate resilience in fighter-jet and robot models.

Abstract

In environments with uncertainties or undesirable influences, control systems can require additional energy to achieve their task while remaining resilient to these influences. In this paper, we present an energetic resilience metric that quantifies the maximal additional energy used by a system under undesired effects, while satisfying complex specifications encoded through temporal logic. We prove that this metric satisfies properties that enable its computation even for compositions of these specifications, thus allowing considerations of sequential reachability and safety tasks. For specifications related to finite-horizon reachability and safety, we describe how synthesizing a control input and computing this metric reduces to solving efficient quadratic programs. Two case studies on a fighter-jet model and a planar mobile robot illustrate how the synthesized control inputs satisfy given specifications despite undesired and potentially adversarial effects. Further, we demonstrate how the energetic resilience metric varies with the initial state as well as the magnitude of undesired effects.