Data-Driven Time-Varying Control Barrier Functions for Adaptive Safe-Set Learning with Online Decremental Support Vector Machines

Shawon Dey; Michael Budihartono; Hever Moncayo

cs.CEAug 19, 2026

Data-Driven Time-Varying Control Barrier Functions for Adaptive Safe-Set Learning with Online Decremental Support Vector Machines

Authors: Shawon Dey, Michael Budihartono, Hever Moncayo

Organizations: Department of Aerospace Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL 32114 USA

Abstract

Mission-critical intelligent systems often operate under time-varying limitations that reduce control authority and change the admissible safe operating envelope. In such settings, a safety certificate learned under nominal conditions may become invalid as system capability changes. To address this challenge, this paper proposes a degradation-aware, data-driven safety-filtering framework that learns a safe set from data, updates it online, and enforces the resulting learned barrier through a time-varying control barrier function (CBF). A nominal safe envelope is first learned from operational data using a radial basis function (RBF)-kernel support vector machine (SVM), whose decision function serves as the initial CBF candidate. To capture capability-induced safe-set contraction, a continuous-time decremental SVM update law is developed so that selected support-vector coefficients are reduced according to a degradation signal. A homotopy-smoothed SVM-CBF is then introduced to avoid discontinuous changes in the learned barrier during active-set transitions. The resulting time-varying learned barrier is enforced using a quadratic-program-based safety filter under degraded input constraints. Forward invariance of the learned time-varying safe set and recursive feasibility of the safety filter are established. Simulation results on a vertical takeoff and landing (VTOL) model show that the proposed method maintains safety under reduced control authority and avoids abrupt barrier-switching effects during safe-set contraction.

Figures & tables

Fig. 1: Safe-set contraction under elevator actuator degradation. As the available elevator authority decreases, the admissible safe envelope in the pitch-state space contracts accordingly.

Fig. 2: Homotopy-smoothed barrier transition. As $\eta_{\ell}(t)$ increases from $0$ to $1$ , the safe-set boundary transitions continuously from $h_{\ell}^{-}(x,t)$ to $h_{\ell+1}^{+}(x,t)$ , yielding a contraction of the safe set in the $(\alpha,q)$ plane.

Fig. 3: Degradation-aware SVM-CBF-QP framework for adaptive safe-set learning and safe control under reduced control authority.

Fig. 4: Evolution of the learned safe envelope under actuator degradation. Circles denote support vectors, and the decremental update removes outer safe support vectors, contracting the envelope.

Fig. 5: Closed-loop trajectory under the proposed time-varying filter overlaid on the shrinking safe set at selected time. The dot marks the current state, and the dashed line denotes the past trajectory.

Fig. 6: State trajectories and elevator command under smooth actuator degradation. Dashed lines indicate the contracting safe limits and degraded input bound.

Fig. 7: Barrier function and filter intervention. The proposed filter maintains $h_{H}(x(t),t)\geq 0$ while intervening only when necessary.

Fig. 8: State trajectories and elevator command under an instantaneous barrier switch at $t=5$ s, with and without the homotopy transition. Dashed and dotted lines denote the enforced state limits.

Fig. 9: Enforced barrier function evaluation. The instantaneous swap produces a jump to $h<0$ , while the homotopy keeps the barrier continuous and nonnegative.

$T^{\mathrm{tr}}$ (s)	Infeasible steps	$\max_{t}\|\Delta u\|$ (rad)
0.05	4	0.3429
0.20	14	0.1581
0.50	7	0.055
1.00	0	0.055
2.00	0	0.055

TABLE I: Effect of transition duration on QP feasibility (Case 2).

Safety-Critical Control

Safety-critical control designs controllers that keep physical systems within hard safety constraints despite uncertainty, disturbances, and limited actuation.

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Safety-Critical Control Control Barrier Functions Robust Control

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Control barrier functions (CBFs) certify commands through an assumed dynamics model, so an abrupt, unmeasured regime change can undermine the certificate exactly when safety matters most. We present Look-Back Adaptive Control Barrier Functions (LBA-CBF), which rank a finite bank of candidate dynamics by recent prediction error over a short look-back window and enforce the high-order CBF condition against every model within a tolerance of the best, spanning best-fit adaptation to full-bank robust filtering. The dynamics may depend nonlinearly on the unknown parameters, and no switching model or continuously parameterized estimator is required. We prove that any feasible filtered input satisfies the true CBF condition whenever a safety-representative candidate is retained. In quadrotor simulation with abrupt wind reversals and an unknown payload, LBA-CBF is safe and reaches the goal from all random initial conditions, matching an oracle, while adaptive and robust baselines achieve 0-88% success. Banks of up to 250,000 models run inside the control loop, and Crazyflie 2.1 and F1TENTH experiments demonstrate adaptation to wind, payload release, and varying tire-road friction. Code, videos, and project details are available at: https://lla-control.github.io

Abstract

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