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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Abstract

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