parametric control barrier function

To address the challenge of jointly ensuring safety and optimizing performance when tuning control barrier function (CBF) parameters in safety-critical control systems, this paper proposes an adaptive parameter-tuning framework integrating CBFs with safety-aware Bayesian optimization (SBO). Our method introduces a novel safety-acquisition function based on the barrier interior-point method, establishes the first taxonomy for CBF parameters, and provides unified theoretical guarantees for both safety satisfaction and optimality. The framework is model-agnostic and supports flexible customization of objectives and constraints. Evaluated on benchmark tasks—including swing-up control of an inverted pendulum and high-fidelity adaptive cruise control—the approach achieves 100% safety-constraint satisfaction while significantly improving closed-loop performance. Results demonstrate its rigorous safety assurance, real-time feasibility, and superior optimization efficiency.

Verifying robust safety of discrete-time Control Barrier Functions (CBFs) in high-dimensional systems suffers from prohibitive computational complexity. Method: We propose a sample-efficient certification framework leveraging Lipschitz continuity. By reformulating the robust constraint verification as a scenario optimization problem and deriving tight bounds on CBF gradient variation via its Lipschitz constant, we drastically reduce the required number of sampling points. A lightweight verification algorithm is further designed to certify that the zero sublevel set satisfies robust forward invariance. Contribution/Results: Compared to conventional grid-based search or conservative approximations, our method achieves sublinear sample complexity while preserving rigorous theoretical safety guarantees. Numerical experiments on multiple nonlinear systems demonstrate that it attains accuracy comparable to full-state-space verification using less than 1% of the samples—significantly enhancing the deployability of CBFs in real-time safety-critical control.

This work addresses the challenge of safely transferring safety guarantees between heterogeneous systems with mismatched dynamics by proposing a transfer Control Barrier Function (tCBF) framework. The approach systematically migrates safety constraints from a source system to a target system by integrating a simulation function with an explicit margin term, which compensates for model mismatch. Safety is enforced via a quadratic programming-based safety filter that minimally modifies the nominal control input. Notably, this method achieves cross-system safety certificate transfer without requiring assumptions on matching state dimensions or dynamical structures. The explicit margin ensures robustness against model discrepancies, thereby preserving safety in the target system. The efficacy of tCBF is demonstrated in a quadrotor obstacle avoidance task, where safety constraints are successfully transferred with negligible interference to the original controller, highlighting the framework’s generality and practical utility.

Real-time safety-critical control of input-constrained systems—particularly for resource-limited aerospace platforms—remains challenging due to the high computational cost of conventional backup Control Barrier Functions (bCBFs), which require online solution of high-dimensional quadratic programs. Method: This paper proposes a closed-loop solvable bCBF framework. We derive, for the first time, an analytical closed-form solution to the bCBF optimization problem by optimally interpolating between a nominal controller and a backup controller, thereby jointly ensuring system safety and input boundedness without runtime numerical optimization. Contribution/Results: The proposed method drastically reduces computational complexity while rigorously enforcing nonlinear safety constraints. Experimental validation on a double-integrator system and a nonlinear fixed-wing aircraft model demonstrates both theoretical safety guarantees and real-time feasibility. This work provides a provably safe, lightweight control solution tailored for computationally constrained platforms.

This work proposes a data-driven framework for safety verification and synthesis tailored to black-box AI systems operating in safety-critical settings with discrete-time stochastic dynamics. By constructing ambiguity sets in a reproducing kernel Hilbert space (RKHS) based on observed system trajectories, the approach leverages conditional mean embeddings to characterize uncertainty without requiring explicit knowledge of the system dynamics or noise distributions. A finite Fourier expansion is employed to transform the resulting semi-infinite optimization problem into a tractable linear program. The framework accommodates general temporal logic specifications and incorporates a distributionally robust mechanism to handle out-of-distribution behaviors. Empirical evaluations on black-box systems—including those with neural network controllers—demonstrate that the method ensures safety while maintaining strong scalability and robustness.

Real-time computation of safety-preserving control inputs for discrete-time systems subject to nonconvex safe sets is challenging due to inherent nonconvexity in the underlying safety constraints. Method: This paper proposes a novel design framework integrating matrix control barrier functions (MCBFs) with convex optimization. We extend MCBFs—originally formulated for continuous-time systems—to discrete-time dynamics and construct an equivalent convex optimization problem via judicious convex relaxation, thereby circumventing direct solution of nonconvex programs while ensuring forward invariance of the safe set. Contribution/Results: The method unifies system dynamics, safety requirements, and convexification techniques to significantly improve computational efficiency and online implementability. Extensive simulations on a quadrotor platform demonstrate the approach’s superiority in safety enforcement, state convergence, and real-time performance. This work establishes a new paradigm for safety-critical control under nonconvex safety constraints.

Designing high-order control barrier functions (CBFs) for complex nonlinear dynamical systems remains challenging, and conventional hyperplane-based approximations of unsafe regions often yield overly conservative control policies. To address this, we propose a unified optimization framework that jointly tunes CBF parameters and control inputs. Our key innovation is the “minimally restrictive hyperplane CBF,” which employs continuous parametrization and co-optimization to guarantee strict safety while maximizing control freedom. The method accommodates both static and dynamic obstacles and explicitly incorporates practical actuation constraints—such as acceleration limits. Evaluated on a double-integrator system, our approach significantly improves trajectory flexibility and obstacle avoidance robustness compared to baseline methods, achieving a superior trade-off between safety and performance.

This work addresses the gap between theoretical safety guarantees and practical feasibility of Control Barrier Functions (CBFs) in real-world systems subject to input constraints, where implicit assumptions often render CBFs ineffective. By systematically distinguishing between candidate and valid CBFs, the study uncovers the true source of safety in passive systems and extends safety verification to non-passive systems. Integrating system dynamics, explicit input constraint modeling, and class-K function analysis, the authors establish precise conditions under which CBFs yield valid safety assurances in low-dimensional systems and derive actionable design principles for safe controllers. An accompanying interactive web platform visually illustrates the core mechanisms and common pitfalls, offering practitioners an intuitive guide for reliable deployment.

This work addresses the challenge of ensuring safe and autonomous robot navigation in complex dynamic environments by proposing a novel “Control Barrier Corridor” framework. It unifies control barrier functions with safety corridors for the first time, reformulating safety constraints as locally feasible target regions. By integrating feedback control with convex optimization, the method generates reference trajectories that guarantee continuous safety in real time. The approach is validated on fully actuated systems, unicycle models, and linear output regulation systems, demonstrating its broad applicability. A key contribution lies in establishing a tunable trade-off between safety and responsiveness, enabling verifiably safe, persistent, and adaptive exploration even in unknown environments.

This work proposes a safety verification method for stochastic dynamical systems operating in the presence of dynamic obstacles, aiming to guarantee—within a finite time horizon and with high probability—that system trajectories remain within a prescribed safe set. The approach introduces time-varying stochastic barrier certificates that explicitly characterize time-dependent unsafe regions and leverages the Bellman optimality principle to model temporal structure, thereby yielding a certifiable lower bound on the probability of safety. By restricting the barrier certificates to polynomial form, the synthesis problem is cast as a convex sum-of-squares (SOS) optimization, enabling efficient computation. Experimental results demonstrate that, compared to existing methods, the proposed framework provides tighter, less conservative safety guarantees for nonlinear systems, achieving both higher accuracy and improved scalability.