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arxiv: 2604.14203 · v1 · submitted 2026-04-03 · 📡 eess.SY · cs.SY

Energetic Resilience under Temporal Logic Specifications

Ratnangshu Das , Ram Padmanabhan , Melkior Ornik , Pushpak Jagtap This is my paper

Pith reviewed 2026-05-13 19:27 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords energetic resiliencetemporal logic specificationscontrol synthesisquadratic programmingresilient controlundesired effectsfinite-horizon specificationsreachability and safety
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The pith

A metric quantifies the maximum extra energy a control system expends to satisfy temporal logic specifications despite undesired effects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper defines an energetic resilience metric for control systems operating under uncertainties or adversarial influences. This metric measures the worst-case additional energy required to fulfill specifications given as temporal logic formulas. It satisfies properties that support composition of specifications, such as combining sequential reachability and safety tasks. For finite-horizon reachability and safety, the metric and the corresponding control synthesis reduce to solving quadratic programs. Illustrations on a fighter-jet model and a planar mobile robot show how the approach works in practice.

Core claim

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.

What carries the argument

The energetic resilience metric, which captures the worst-case extra energy cost under undesired influences while meeting temporal logic constraints.

If this is right

  • The metric enables analysis of composed specifications for sequential reachability and safety tasks.
  • Both the control input synthesis and the metric computation reduce to efficient quadratic programs for finite-horizon reachability and safety.
  • Synthesized controls continue to satisfy the given specifications even in the presence of undesired and potentially adversarial effects.
  • The value of the metric changes predictably with different initial states and different magnitudes of undesired effects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This metric could guide energy budgeting in the design of autonomous vehicles or aircraft that must maintain performance against interference.
  • The approach might extend to nonlinear dynamics if similar convex relaxations can be found, though the paper focuses on the linear-quadratic case.
  • Treating undesired effects as adversarial players could link the metric to existing robust control or game-theoretic methods.

Load-bearing premise

The system dynamics and cost structures allow control synthesis and metric computation to be reduced to convex quadratic programs for finite-horizon reachability and safety specifications.

What would settle it

A concrete example where the quadratic program either fails to produce a control input that satisfies the temporal logic specification under disturbance or yields an energy cost that violates the claimed composition properties for sequential tasks.

Figures

Figures reproduced from arXiv: 2604.14203 by Melkior Ornik, Pushpak Jagtap, Ram Padmanabhan, Ratnangshu Das.

Figure 1
Figure 1. Figure 1: ADMIRE system under the finite-horizon safety specification [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: ADMIRE system under the exact-time reachability specification [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mobile robot under a sequential reachability task. The robot sequentially reaches [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Heatmap of energetic resilience over a grid of initial conditions for the mobile robot. Lower values near the [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Energetic resilience as a function of disturbance magnitude [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces an energetic resilience metric that quantifies the maximal additional energy a control system expends to satisfy temporal logic specifications in the presence of undesired or adversarial effects. It proves properties of the metric that support computation for composed specifications (e.g., sequential reachability and safety tasks) and reduces finite-horizon reachability and safety synthesis plus metric evaluation to quadratic programs. Two case studies (fighter-jet model and planar mobile robot) illustrate control synthesis and metric variation with initial state and disturbance magnitude.

Significance. If the metric properties hold and the QP reductions are valid under the requisite modeling assumptions, the work offers a quantifiable, composable measure of energy overhead for resilient control under temporal logic constraints. This could be useful for linear-quadratic systems where tractable synthesis is needed for complex tasks; the case studies provide concrete illustrations of the metric's behavior.

major comments (2)
  1. [Abstract] Abstract: the reduction of synthesis and metric computation to efficient quadratic programs for finite-horizon reachability and safety is asserted without explicit statement of the required modeling assumptions (linear/affine dynamics and quadratic costs). These assumptions are load-bearing for convexity and efficiency; outside the linear-quadratic regime the claimed tractability for composed specifications does not hold.
  2. [Abstract] Abstract and proofs section: the metric is introduced by definition with asserted properties enabling composition, but the full derivations, error bounds, and explicit assumptions are not visible in the provided text. This prevents verification of whether the properties preserve the QP structure for the claimed cases.
minor comments (1)
  1. [Abstract] Abstract: add one sentence stating the system class (linear dynamics, quadratic costs) for which the QP reduction is valid to clarify scope.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and have revised the manuscript to explicitly state modeling assumptions in the abstract while clarifying references to the proofs.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the reduction of synthesis and metric computation to efficient quadratic programs for finite-horizon reachability and safety is asserted without explicit statement of the required modeling assumptions (linear/affine dynamics and quadratic costs). These assumptions are load-bearing for convexity and efficiency; outside the linear-quadratic regime the claimed tractability for composed specifications does not hold.

    Authors: We agree that the assumptions should be stated explicitly. The work assumes linear/affine dynamics and quadratic costs, which ensure convexity and allow reduction to quadratic programs. We have revised the abstract to include these assumptions and note that the composition properties and tractability claims are specific to this setting. revision: yes

  2. Referee: [Abstract] Abstract and proofs section: the metric is introduced by definition with asserted properties enabling composition, but the full derivations, error bounds, and explicit assumptions are not visible in the provided text. This prevents verification of whether the properties preserve the QP structure for the claimed cases.

    Authors: The metric definition, composition properties, full derivations, and proofs appear in Sections III and IV, with modeling assumptions in Section II. We have updated the abstract to reference these sections explicitly and confirm that the properties preserve the QP structure under the linear-quadratic assumptions as shown in the proofs. revision: partial

Circularity Check

0 steps flagged

No significant circularity; metric defined directly with independent proofs and QP reductions

full rationale

The energetic resilience metric is introduced as an explicit definition quantifying maximal additional energy under undesired effects while satisfying temporal logic specifications. Properties enabling computation for composed specifications are proved directly. For finite-horizon reachability and safety, synthesis and metric computation are reduced to quadratic programs via standard convex optimization under the system's dynamics and costs. No self-definitional loops appear (metric not defined via its own outputs), no fitted parameters are relabeled as predictions, and no load-bearing self-citations or imported uniqueness theorems are invoked in the provided text. The derivation chain relies on independent definitions, proofs, and reductions rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the new definition of the metric plus standard assumptions from control theory that permit the QP reduction; no free parameters, invented entities, or ad-hoc axioms are visible in the abstract.

axioms (1)
  • domain assumption Finite-horizon reachability and safety specifications under the given dynamics admit reduction to quadratic programs
    Invoked to obtain efficient computation of the metric and control inputs.

pith-pipeline@v0.9.0 · 5450 in / 1189 out tokens · 33588 ms · 2026-05-13T19:27:17.878044+00:00 · methodology

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