Finite-Data Safety Informativity Under Dynamic Asymmetric Actuation
Authors: Abhinav Sinha, Praveen Kumar Ranjan, Yongcan Cao
Organizations: GALACxIS Lab, Department of Aerospace Engineering, University of Cincinnati, Cincinnati, OH 45221, USA · Unmanned Systems Lab (USL), Department of Electrical Engineering, The University of Texas at San Antonio, TX 78249, USA
When the system model is not fully known, measurement error and limited excitation can leave several models consistent with the same finite data. A command judged safe for one model may fail for another, while limited control authority can prevent the corrective action needed to preserve safety. To ensure safety under model uncertainty and asymmetric input limits, we develop a finite-data certificate that determines whether a command can enforce a prescribed safety inequality. For a linearly parameterized safety channel with exactly known regressors and bounded aggregate residual error, we derive a support formula for the worst-case safety contribution of all data-consistent models. The formula identifies the regressor directions that admit a finite bound, allowing rank-deficient records to contribute to safety certification. Using certified componentwise bounds on actuator tracking error yields an affine inequality with a necessary and sufficient test for pointwise command feasibility. The affine inequality reduces computation of the closest certified command to a scalar root-finding problem. It also yields a closed-form gate that selects the largest certified fraction of a prescribed command segment. The proposed certificate guarantees output safety within its operating domain, provided the feedback is locally Lipschitz and the uncertainty bounds remain valid. Domain retention and full-state continuation extend this guarantee to all time. A vehicle study demonstrates that output safety can be certified from finite measurements in a safety-critical setting with model and actuator uncertainty.
Figures & tables
Fig. 1 : Position tracking with asymmetric error bounds.
Fig. 2 : Effect of dataset selection on safety informativity.
Fig. 3 : Closed-loop performance of the data-driven controller.
We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-∞ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-∞ performance balance accounts for the accumulated deviation of the applied input from the baseline H-∞ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.
Muhamad Rausyan Fikri
Faculty of Engineering and Natural Sciences, Tampere University, 33720 Tampere, Finland
Sim-to-real policies are designed under nominal dynamics, but target-system trials may yield only a few isolated one-step transitions. We study pre-execution certification of a fixed control sequence, such as an action chunk produced by a learned policy. If the sequence reaches an unobserved state-input region, the observations remain consistent with target systems whose trajectories separate along it by an arbitrarily large amount. Any deterministic certifier sound for all of them must then decline to certify or return a reachable tube with arbitrarily large projected width. For bounded smooth classes of the target-nominal model error, we derive a finite plan-dependent projected-width lower bound. These results expose a trilemma among uniform trajectory containment, finite projected width, and unrestricted model-error behavior beyond the observations. ForeReach requires a supplied componentwise Lipschitz bound on the model error. Observed transition pairs can refute this declaration but cannot establish it outside the observed locations. Conditional on a valid declaration, our method constructs a set-membership envelope for the model error, propagates a zonotopic reachable tube, and certifies only when propagation remains within the certification domain and every projected tube slice avoids the unsafe set. In two benchmark systems, calibration baselines may remain narrow after losing trajectory containment outside data support, whereas our method declines to certify unsupported sequences and recovers certification when relevant target data and sufficient obstacle clearance are available.
Yanliang Huang, Zhen Zhang, Ahmad Hafez +4
School of Computation, Information and Technology, Technical University of Munich, Munich, Germany · School of Engineering, Hainan Bielefeld University of Applied Sciences, Hainan, China
The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming (DP). This recursion may lead to compounding errors in the certified safety probability, thus collapsing to a vacuous lower bound for growing horizons T. We propose a kernel embedding framework that treats safety certification as a classification problem on trajectory data, directly estimating the T-step safety probability without recursion. We show that the framework subsumes well-established approaches from the literature (e.g., barrier certificates, robust Markov models) as special cases, and allows us to go beyond their limitations. As the main consequence, it bypasses compounding error across the horizon and enables certification for systems with non-Markovian dynamics. We demonstrate that direct estimators remain stable independent of the certification horizon and in the non-Markovian setting, whilst DP-based certificates silently go unsound -- confirmed in simulation on a neural-controlled quadrotor.
Oliver Schön, Licio Romao, Sadegh Soudjani
ETH Zürich · Zürich, Switzerland · Technical University of Denmark +3