Finite-Data Safety Informativity Under Dynamic Asymmetric Actuation
This preprint presents a finite-data safety certificate that checks whether a commanded input can keep a partially unknown nonlinear system within prescribed output bounds even when actuators have asymmetric limits and bounded tracking error. In a simulated vehicle-tracking study, a data-selection strategy produced certificates at 76.27% of 11,241 validation queries, versus 32.09% for uniformly sampled and 1.03% for consecutively sampled records, and an exact-parameter benchmark reached 86.26%. The work matters because it gives a deterministic, model-uncertainty-aware safety filter for high-assurance control where a reliable dynamics model is unavailable.
Can finite measurements of a partially unknown nonlinear system certify whether an admissible command can enforce a prescribed output-safety inequality under asymmetric actuator limits and bounded actuator tracking error?
When the system model is only partially known, several models can remain consistent with the same finite data, so a command judged safe for one model may fail for another. At the same time, limited or asymmetric control authority, plus actuator tracking error, can prevent the corrective action needed to preserve safety. Existing safety methods typically rely on a trusted model or on probabilistic/estimated uncertainty bounds, but do not establish that a finite data record is sufficient to certify safety for every data-consistent model under limited actuator authority.
Earlier approaches include control barrier function safety filters, predictive safety optimization, Gaussian-process uncertainty bounds, reinforcement-learning corrections, conformal calibration, robust adaptive uncertainty estimation, and data informativity for linear systems. Actuator-aware formulations such as admissibility-preserving input realization embed asymmetric limits and quantify tracking-error margins. Their main shortcoming is that they either assume a sufficiently accurate model or provide probabilistic/estimated bounds rather than a deterministic worst-case certificate over all models consistent with finite data and all admissible actuator errors.
The paper models the unknown safety-channel contribution as a linearly parameterized term with exactly known regressors and a bounded aggregate residual. It derives a support formula that gives the worst-case data-consistent model contribution at a query, distinguishing directions where the bound is finite from directions where the uncertainty is unbounded. It then adds certified componentwise actuator-error bounds to obtain an affine command inequality with a necessary and sufficient pointwise feasibility test. This reduces the closest certified command to a scalar root-finding problem and yields a closed-form gate for the largest certified fraction of a desired command segment. A data-selection rule, used in the numerical study, picks a fixed number of samples from a larger flight campaign by favoring weakly represented regressor directions.
The certificate was evaluated on 11,241 state-time validation queries in a 2D vehicle-tracking simulation with structured wind and turbulence. With 40-sample records, pointwise actuator-aware coverage was 1.03% for the consecutive record, 32.09% for the uniformly spaced record, and 76.27% for the certificate-directed record; an exact-parameter benchmark certified 86.26%, leaving a 9.99 percentage-point gap. Median finite-data excess dropped from 2.423 s^-1 for consecutive sampling to 0.1477 s^-1 for uniform sampling and 0.0353 s^-1 for directed sampling. In a 20-second closed-loop run starting with W(0)=0.7349, tracking errors entered and stayed within [-0.2,0.2] m by 3.05 s and 4.25 s for horizontal and vertical errors, the maximum sampled storage remained 0.7349, realized inputs stayed within approximately [9,14] m/s horizontally and [-1.856,1.044] m/s vertically, and the desired command was fully admitted from about 0.1 s to 2.44 s before being blended toward the certified projection. Halving the integration step changed settling times by 0.0025 s.
The validation is simulation-only on a single low-dimensional vehicle model, not real hardware. The method requires exactly known regressors, a fixed parameter matrix, input-independent features, and a valid bounded-residual/measurement-error bound throughout the operating domain. Out-of-span query directions are not certified for nonzero safety functionals. The actuator-error reserve can be conservative because it maximizes over the full error box, and the decay certificate is stronger than output safety; a counterexample shows pointwise feasibility does not guarantee a continuous safe feedback selector. All-time safety requires additional boundedness and domain-retention conditions. No code release or compute-cost data is reported in the paper.
The approach could inform safety-filter and high-assurance control layers for drones, eVTOL aircraft, autonomous ground vehicles, and industrial robotics integrators that must operate with partial models and limited actuation. Near-term use is most plausible in simulation-based verification and aerospace GNC research tooling; real-world deployment is likely 3+ years away and would require physical validation, less restrictive regressor/uncertainty assumptions, and evidence that the certificate can be computed at useful control rates.
The full text is not republished here because the paper's license does not allow it. Read the original on arXiv.