Energetic Resilience under Temporal Logic Specifications
This work provides a formal metric for energy resilience in control systems with complex temporal logic specifications, enabling systematic trade-off analysis for safety-critical applications.
The paper introduces an energetic resilience metric that quantifies the maximal additional energy a control system uses under undesired effects while satisfying temporal logic specifications. The metric is computable for compositions of specifications and reduces to efficient quadratic programs for finite-horizon reachability and safety tasks, demonstrated on a fighter-jet and a mobile robot.
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.