control barrier functions

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.

Addressing the challenge of achieving both high performance and formal safety guarantees for high-dimensional autonomous systems in real-world environments, this paper proposes a two-stage co-optimization framework. In the first stage, state constraints are relaxed into penalty terms within a gradient-based model predictive control (MPC) formulation, enhancing computational efficiency and scalability. In the second stage, a safety-critical control barrier function (CBF)-based filter is constructed and implemented via quadratic programming (QP) to minimally modify a reference controller while strictly enforcing hard safety constraints. The method innovatively integrates gradient optimization, relaxed safety-constrained optimal control problems (SC-OCPs), and CBF-QP filtering—thereby reconciling high-performance control with formal safety certification, while avoiding the excessive conservatism and computational infeasibility common in conventional safety filters. The approach is validated on two high-dimensional, complex dynamical systems.

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.

Ensuring safety for nonlinear affine systems under complex, uncertain disturbances remains challenging. Method: This paper proposes a robust safety controller that integrates uncertainty estimation with high-order control barrier functions (HOCBFs). It innovatively embeds bounds on estimation errors directly into the CBF constraints and extends the formulation to a second-order cone programming (SOCP) framework. The approach unifies elastic actuator modeling, HOCBF-based safety constraints, and quadratic-programming (QP) feedback control. Contribution/Results: It is the first method to provide rigorous robust safety guarantees against both matched and mismatched disturbances. Evaluations in simulation and on a tracked robot navigating inclined terrain demonstrate 100% safety constraint satisfaction, a 42% improvement in disturbance rejection, and significantly enhanced motion robustness and real-time safety under dynamic uncertainties.

Neural network dynamic models (NNDMs) pose significant challenges for safety verification due to their nonlinearity, stochasticity, and lack of provable probabilistic safety guarantees. Method: This paper introduces a theoretical framework based on stochastic barrier functions (SBFs), the first application of SBFs to NNDM analysis. It integrates convex neural network approximations with piecewise-linear bounding techniques to enable automated synthesis of barrier functions, and designs a minimally invasive linear programming controller to tighten the lower bound on system safety probability. The approach unifies sum-of-squares (SOS) optimization with robust control synthesis, supporting high-dimensional, deep NNDMs (e.g., up to hundreds of neurons per layer). Results: Experiments demonstrate substantial improvements in certified safety probability, achieving efficient and formally verifiable safety guarantees. The method establishes the first safety verification paradigm for noisy iterative-prediction neural dynamic systems that simultaneously ensures theoretical rigor and computational tractability.

Existing control barrier function (CBF) approaches rely on explicit structural knowledge of system dynamics and uncertainty models, limiting their applicability to general nonlinear systems and often yielding overly conservative safe sets. This work proposes a model-free robust Q-CBF framework that, for the first time, integrates the safety value function with the Q-function to formulate robust safety constraints directly in the state-action space. By leveraging adversarial reinforcement learning and solving the associated Hamilton–Jacobi–Isaacs equation, the method computes the largest possible robustly safe set. Evaluations on an inverted pendulum and a 36-dimensional quadrupedal robot demonstrate that the proposed approach significantly reduces conservatism and achieves more reliable safe control under unknown disturbances.

This work addresses the challenge of enforcing hard affine state constraints in black-box hybrid dynamical systems subject to instantaneous state jumps and unknown nonlinear dynamics. To this end, the authors propose a novel reinforcement learning strategy that incorporates an affine repulsion mechanism near constraint boundaries and introduces a secondary repulsion region just before the system’s reset map. This approach ensures strict satisfaction of safety constraints in closed-loop operation without requiring an explicit system model. Notably, it establishes the first provably safe reinforcement learning framework for black-box hybrid systems, effectively mitigating constraint violations induced by state discontinuities. Empirical evaluations on benchmark tasks—including a constrained pendulum and a juggling paddle system—demonstrate that the proposed method consistently guarantees constraint satisfaction while learning superior policies compared to existing reward-shaping and control barrier function–based approaches.

This work addresses the challenge of achieving semi-global feedback control for high-dimensional nonlinear systems under hard safety constraints. The authors propose a novel approach that integrates a control barrier function (CBF)-based safety filter directly into end-to-end policy training. By leveraging operator splitting and Jacobian-free backpropagation (JFB), the method effectively circumvents the computational and differentiability bottlenecks associated with conventional CBF optimization layers in high-dimensional settings. This framework enables, for the first time, safe end-to-end learning in state spaces with over a thousand dimensions. Demonstrated on a multi-agent system with state and control dimensions as high as 1200 and 400, respectively, the approach achieves optimal feedback control that simultaneously guarantees rigorous safety and supports efficient training.

This work addresses the challenges of traditional constrained control methods, which rely on online optimization and often fail to guarantee recursive feasibility. To overcome these limitations, the paper proposes a safety-aware control framework that integrates an Explicit Reference Governor (ERG) with Control Barrier Functions (CBFs). By modeling reference updates as virtual control inputs of an augmented system and constructing a smooth barrier function based on dynamic safety margins and soft-min aggregation, the approach achieves closed-loop safety without requiring online optimization. Recursive feasibility of safety constraints is ensured at the design level through the forward invariance of Lyapunov sublevel sets, yielding an explicit, closed-form reference update law. Theoretical analysis establishes asymptotic convergence of the closed-loop system, and simulations demonstrate that the proposed method maintains rigorous safety guarantees while achieving performance comparable to conventional ERG schemes.

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.