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arxiv: 2604.14714 · v1 · submitted 2026-04-16 · 📡 eess.SY · cs.SY

Temporal Logic Resilience for Continuous-time Systems

Ratnangshu Das , Negar Monir , Youssef Ait Si , Adnane Saoud , Sadegh Soudjani , Pushpak Jagtap This is my paper

Pith reviewed 2026-05-10 11:18 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords resiliencesignal temporal logiccontinuous-time systemsdisturbance boundsscenario optimizationsystem verificationnonlinear dynamics
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The pith

A framework computes lower bounds on the maximum disturbance continuous-time systems can tolerate while satisfying signal temporal logic specifications.

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

The paper develops a method to quantify resilience in continuous-time systems that must obey signal temporal logic rules in the presence of external disturbances. Resilience is the largest disturbance magnitude the system can absorb from a given initial state without violating the logic specification. The approach first derives bounds on how trajectories are perturbed by disturbances and then embeds these bounds into a scenario optimization problem to calculate a guaranteed lower bound on the maximum admissible disturbance. This matters for engineered systems like motors and vehicles that must maintain time-dependent behaviors such as collision avoidance or temperature regulation under uncertainty. The framework is tested on linear, nonlinear, and hybrid examples to show its applicability.

Core claim

The paper establishes a computational framework that derives explicit bounds on perturbed trajectories of continuous-time nonlinear systems and incorporates them into a scenario optimization program, thereby computing a lower bound on the maximum admissible disturbance that still ensures satisfaction of a given signal temporal logic specification from a fixed initial state.

What carries the argument

Bounds on perturbed trajectories derived from the system dynamics, used to formulate a scenario optimization problem that yields a lower bound on the maximum admissible disturbance.

If this is right

  • The computed bound certifies that all disturbances up to that level will preserve satisfaction of the temporal logic specification.
  • Scenario optimization enables efficient calculation without enumerating the entire disturbance space.
  • The method applies directly to both linear and nonlinear continuous-time dynamics as demonstrated in the motor, temperature, and vehicle examples.
  • Designers obtain a conservative yet computable resilience margin that can guide controller tuning.

Where Pith is reading between the lines

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

  • The same trajectory-bound technique could be adapted to estimate resilience under bounded parametric uncertainty in addition to additive disturbances.
  • Integration with model predictive control might allow online adjustment of the resilience margin during operation.
  • The lower bound could serve as a constraint in optimization-based synthesis of controllers that maximize resilience while meeting other performance goals.

Load-bearing premise

Bounds on perturbed trajectories can be derived for the system class and scenario optimization produces a reliable lower bound on the maximum admissible disturbance.

What would settle it

A concrete counterexample in which a disturbance smaller than the computed bound causes violation of the signal temporal logic specification from the given initial state would disprove the lower-bound claim.

Figures

Figures reproduced from arXiv: 2604.14714 by Adnane Saoud, Negar Monir, Pushpak Jagtap, Ratnangshu Das, Sadegh Soudjani, Youssef Ait Si.

Figure 1
Figure 1. Figure 1: Comparison of bounds obtained using the proposed approach, element-wise absolute-value bounds, and [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of 1000 perturbed trajectories in the DC Motor case. Green lines mark the safe and target set [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of 1000 perturbed trajectories in the temperature regulation case. Green and blue correspond to the [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of 1000 perturbed trajectories starting from [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Carla simulation environment with the fire truck [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
read the original abstract

In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike robustness, which evaluates how well a system satisfies a specification under a given disturbance, resilience measures the maximum disturbance a system can tolerate from a given initial state while maintaining specification satisfaction. We first derive bounds on the perturbed trajectories and then use them to formulate a computational method based on scenario optimization to efficiently compute the maximum admissible disturbance. We validate our approach through case studies, including dc motor, temperature regulation, a nonlinear numerical example, and a vehicle collision avoidance case.

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

0 major / 3 minor

Summary. The paper presents a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic (STL) specifications. Resilience is defined as the maximum disturbance tolerable from a given initial state while maintaining STL satisfaction. The approach first derives bounds on perturbed trajectories and then formulates a scenario optimization problem to compute the maximum admissible disturbance efficiently. The method is validated on case studies including a DC motor, temperature regulation, a nonlinear numerical example, and vehicle collision avoidance.

Significance. If the trajectory bounds and scenario optimization steps are sound, the framework provides a practical computational tool for assessing resilience in safety-critical systems with temporal logic constraints, bridging robustness analysis and disturbance tolerance. The use of scenario optimization for efficient lower-bound computation and the diversity of case studies (linear, nonlinear, and control applications) are strengths that support broader applicability in systems and control.

minor comments (3)
  1. [§3] §3 (trajectory bounds derivation): the transition from the nominal system to the perturbed trajectory bound should explicitly state the Lipschitz or growth conditions assumed on the vector field to ensure the bound holds for the full class of nonlinear systems considered.
  2. [Table 1] Table 1 (DC motor results): the reported resilience lower bound is given without the corresponding scenario sample size or violation probability; adding these would strengthen the connection to the scenario optimization guarantee in §4.
  3. [§5.3] §5.3 (vehicle collision avoidance): the STL formula for the specification is referenced but not written out; including the explicit predicate and temporal operators would improve reproducibility of the case study.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work and the recommendation for minor revision. The referee correctly identifies the core contribution: a framework that derives perturbed trajectory bounds for continuous-time systems and then applies scenario optimization to compute a lower bound on the maximum tolerable disturbance while preserving STL satisfaction. We appreciate the recognition of the method's applicability to both linear and nonlinear systems as well as its relevance to safety-critical control problems.

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent trajectory bounds and scenario optimization

full rationale

The paper derives bounds on perturbed trajectories from the system dynamics and then applies scenario optimization to compute a lower bound on the maximum admissible disturbance while preserving STL satisfaction. This chain does not reduce any claimed prediction or resilience value to a fitted parameter or self-referential definition by construction. No self-citation is load-bearing for the central result, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in. The case studies (DC motor, temperature regulation, nonlinear example, vehicle collision avoidance) are presented as validation of the external bounds and optimization procedure rather than tautological outputs. The framework is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; technical details on system assumptions and bounding derivations are absent.

pith-pipeline@v0.9.0 · 5419 in / 991 out tokens · 34132 ms · 2026-05-10T11:18:28.706886+00:00 · methodology

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Reference graph

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