arXiv subjects

Tamas G. Molnar

Publications and source records attributed to Tamas G. Molnar.

At least 19 recordsLinked to original sources

arXiv2026

Uncertainty Estimators for Robust Backup Control Barrier Functions

Designing safe controllers is crucial and notoriously challenging for input-constrained safety-critical control systems. Backup control barrier functions offer an approach for the construction of safe controllers online by considering the flow of the system under a backup controller. However, in the presence of model uncertainties, the flow cannot be accurately computed, making this method insufficient for safety assurance. To tackle this shortcoming, we integrate backup control barrier functions with uncertainty estimators and calculate the flow under a reconstruction of the model uncertainty while refining this estimate over time. We prove that the controllers resulting from the proposed Uncertainty Estimator Backup Control Barrier Function (UE-bCBF) approach guarantee safety, are robust to unknown disturbances, and satisfy input constraints.

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arXiv2026

Robust Adaptive Backup Control Barrier Functions

We propose a notion of robust adaptive backup control barrier functions for nonlinear control affine systems with parametric uncertainty in both the drift dynamics and actuation matrix. Backup control barrier functions guarantee safety by predicting the system's trajectory under a pre-certified safe controller. However, these predictions rely on the model and can be inaccurate when the system contains unknown parameters. To address this issue, we estimate the unknown parameters using element-wise certified adaptive estimators that provide a parameter adaptation law and component-wise estimation error bounds. We compute the backup flow using the estimated model and tighten the safety conditions using these certified bounds. The resulting safety conditions account for the sensitivity of the predicted flow to parameter estimation errors. Moreover, to handle uncertainty in the actuation matrix, we use a duality-based reformulation that enables the use of a computationally efficient quadratic-program-based safety filter. We prove that controllers satisfying the proposed robust adaptive backup control barrier function constraints guarantee safety under parametric uncertainty and input constraints.

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arXiv2026

Output Feedback Backup Control Barrier Functions: Safety Guarantees Under Input Bounds and State Estimation Error

Guaranteeing the safety of controllers is vital for real-world applications, but is markedly difficult when the states are not perfectly known and when the control inputs are bounded. Backup control barrier functions (bCBFs) use predictions of the flow under a prescribed controller to achieve safety in the presence of bounded inputs and perfect state information. However, when only an estimate of the true state is known, this flow may not be precisely computed, as the initial condition is unknown. Furthermore, the true flow evolves using feedback from the estimated state, thus introducing coupling between known and unknown flows. To address these challenges, we propose a technique that leverages an uncertainty envelope centered around the estimated flow and show that ensuring the safety of this envelope guarantees that the true state satisfies the safety constraints. Additionally, we show that in the presence of state uncertainty, using the resulting Output Feedback Backup Control Barrier Functions (O-bCBFs), there always exists a feasible control input that can guarantee the safety of the true state, even in the presence of input constraints.

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arXiv2026

Safety Guardrails in the Sky: Realizing Control Barrier Functions on the VISTA F-16 Jet

The advancement of autonomous systems -- from legged robots to self-driving vehicles and aircraft -- necessitates executing increasingly high-performance and dynamic motions without ever putting the system or its environment in harm's way. In this paper, we introduce Guardrails -- a novel runtime assurance mechanism that guarantees dynamic safety for autonomous systems, allowing them to safely evolve on the edge of their operational domains. Rooted in the theory of control barrier functions, Guardrails offers a control strategy that carefully blends commands from a human or AI operator with safe control actions to guarantee safe behavior. To demonstrate its capabilities, we implemented Guardrails on an F-16 fighter jet and conducted flight tests where Guardrails supervised a human pilot to enforce g-limits, altitude bounds, geofence constraints, and combinations thereof. Throughout extensive flight testing, Guardrails successfully ensured safety, keeping the pilot in control when safe to do so and minimally modifying unsafe pilot inputs otherwise.

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arXiv2026

Integral Control Barrier Functions with Input Delay: Prediction, Feasibility, and Robustness

Time delays in feedback control loops can cause controllers to respond too late, and with excessively large corrective actions, leading to unsafe behavior (violation of state constraints) and controller infeasibility (violation of input constraints). To address this problem, we develop a safety-critical control framework for nonlinear systems with input delay using dynamically defined (integral) controllers. Building on the concept of Integral Control Barrier Functions (ICBFs), we concurrently address two fundamental challenges: compensating the effect of delays, while ensuring feasibility when state and input constraints are imposed jointly. To this end, we embed predictor feedback into a dynamically defined control law to compensate for delays, with the predicted state evolving according to delay-free dynamics. Then, utilizing ICBFs, we formulate a quadratic program for safe control design. For systems subject to simultaneous state and input constraints, we derive a closed-form feasibility condition for the resulting controller, yielding a compatible ICBF pair that guarantees forward invariance under delay. We also address robustness to prediction errors (e.g., caused by delay uncertainty) using tunable robust ICBFs. Our approach is validated on an adaptive cruise control example with actuation delay.

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arXiv2026

Generalizations of Backup Control Barrier Functions: Expansion and Adaptation for Input-Bounded Safety-Critical Control

Guaranteeing the safety of nonlinear systems with bounded inputs remains a key challenge in safe autonomy. Backup control barrier functions (bCBFs) provide a powerful mechanism for constructing controlled invariant sets by propagating trajectories under a pre-verified backup controller to a forward invariant backup set. While effective, the standard bCBF method utilizes the same backup controller for both set expansion and safety certification, which can restrict the expanded safe set and lead to conservative dynamic behavior. In this study, we generalize the bCBF framework by separating the set-expanding controller from the verified backup controller, thereby enabling a broader class of expansion strategies while preserving formal safety guarantees. We establish sufficient conditions for forward invariance of the resulting implicit safe set and show how the generalized construction recovers existing bCBF methods as special cases. Moreover, we extend the proposed framework to parameterized controller families, enabling online adaptation of the expansion controller while maintaining safety guarantees in the presence of input bounds.

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arXiv2026

Enforcing Mixed State-Input Constraints with Multiple Backup Control Barrier Functions: A Projection-based Approach

Ensuring the safety of control systems often requires the satisfaction of constraints on states (such as position or velocity), control inputs (such as force), and a mixture of states and inputs (such as power that depends on both velocity and force). This paper presents a safety-critical control framework for enforcing mixed state-input constraints through a generalization of backup control barrier functions (backup CBFs). First, we extend the backup CBF approach to maintain multiple decoupled state and input constraints using a single backup set-backup controller pair. Second, we address mixed state-input constraints by converting them into state constraints using a projection from the state-input space to the state space along the backup controller. In the special case of decoupled state and input constraints, the proposed method simplifies the synthesis of backup CBFs by eliminating the need for saturating backup control laws. Finally, we demonstrate the efficacy of the proposed method on an inverted pendulum example, where constraints on the angle (state), torque (input), and power (mixture of state and input) are satisfied simultaneously.

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arXiv2025

Combinatorial Control Barrier Functions: Nested Boolean and p-choose-r Compositions of Safety Constraints

This paper investigates the problem of composing multiple control barrier functions (CBFs) -- and matrix control barrier functions (MCBFs) -- through logical and combinatorial operations. Standard CBF formulations naturally enable conjunctive (AND) combinations, but disjunctive (OR) and more general logical structures introduce nonsmoothness and possibly a combinatorial blow-up in the number of logical combinations. We introduce the framework of combinatorial CBFs that addresses p-choose-r safety specifications and their nested composition. The proposed framework ensures safety for the exact safe set in a scalable way, using the original number of primitive constraints. We establish theoretical guarantees on safety under these compositions, and we demonstrate their use on a patrolling problem in a multi-agent system.

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arXiv2025

Braking within Barriers: Constructive Safety-Critical Control for Input-Constrained Vehicles via the Backup Set Method

This paper presents a safety-critical control framework to maintain bounded lateral motions for vehicles braking on asymmetric surfaces. We synthesize a brake controller that assists drivers and guarantees safety against excessive lateral motions (i.e., prevents the vehicle from spinning out) while minimizing the stopping distance. We address this safety-critical control problem in the presence of input constraints, since braking forces are limited by the available friction on the road. We use backup control barrier functions for safe control design. As this approach requires the construction of a backup set and a backup controller, we propose a novel, systematic method to creating valid backup set-backup controller pairs based on feedback linearization and continuous-time Lyapunov equations. We use simple examples to demonstrate our proposed safety-critical control method. Finally, we implement our approach on a four-wheel vehicle model for braking on asymmetric surfaces and present simulation results.

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arXiv2025

Safety-Critical Control with Bounded Inputs: A Closed-Form Solution for Backup Control Barrier Functions

Verifying the safety of controllers is critical for many applications, but is especially challenging for systems with bounded inputs. Backup control barrier functions (bCBFs) offer a structured approach to synthesizing safe controllers that are guaranteed to satisfy input bounds by leveraging the knowledge of a backup controller. While powerful, bCBFs require solving a high-dimensional quadratic program at run-time, which may be too costly for computationally-constrained systems such as aerospace vehicles. We propose an approach that optimally interpolates between a nominal controller and the backup controller, and we derive the solution to this optimization problem in closed form. We prove that this closed-form controller is guaranteed to be safe while obeying input bounds. We demonstrate the effectiveness of the approach on a double integrator and a nonlinear fixed-wing aircraft example.

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arXiv2025

Activated Backstepping with Control Barrier Functions for the Safe Navigation of Automated Vehicles

This paper introduces a novel safety-critical control method through the synthesis of control barrier functions (CBFs) for systems with high-relative-degree safety constraints. By extending the procedure of CBF backstepping, we propose activated backstepping - a constructive method to synthesize valid CBFs. The novelty of our method is the incorporation of an activation function into the CBF, which offers less conservative safe sets in the state space than standard CBF backstepping. We demonstrate the proposed method on an inverted pendulum example, where we explain the underlying geometric meaning in the state space and provide comparisons with existing CBF synthesis techniques. Finally, we implement our method to achieve collision-free navigation for automated vehicles using a kinematic bicycle model in simulation.

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arXiv2025

On the Properties of Optimal-Decay Control Barrier Functions

Control barrier functions provide a powerful means for synthesizing safety filters that ensure safety framed as forward set invariance. Key to CBFs' effectiveness is the simple inequality on the system dynamics: $\dot{h} \geq - α(h)$. Yet determining the class $\mathcal{K}^e$ function $α$ is a user defined choice that can have a dramatic effect on the resulting system behavior. This paper formalizes the process of choosing $α$ using optimal-decay control barrier functions (OD-CBFs). These modify the traditional CBF inequality to: $\dot{h} \geq - ωα(h)$, where $ω\geq 0$ is automatically determined by the safety filter. A comprehensive characterization of this framework is elaborated, including tractable conditions on OD-CBF validity, control invariance of the underlying sets in the state space, forward invariance conditions for safe sets, and discussion on optimization-based safe controllers in terms of their feasibility, Lipschitz continuity, and closed-form expressions. The framework also extends existing higher-order CBF techniques, addressing safety constraints with vanishing relative degrees. The proposed method is demonstrated on a satellite control problem in simulation.

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arXiv2025

Navigating Polytopes with Safety: A Control Barrier Function Approach

Collision-free motion is a fundamental requirement for many autonomous systems. This paper develops a safety-critical control approach for the collision-free navigation of polytope-shaped agents in polytope-shaped environments. A systematic method is proposed to generate control barrier function candidates in closed form that lead to controllers with formal safety guarantees. The proposed approach is demonstrated through simulation, with obstacle avoidance examples in 2D and 3D, including dynamically changing environments.

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arXiv2025

Collision Avoidance and Geofencing for Fixed-wing Aircraft with Control Barrier Functions

Safety-critical failures often have fatal consequences in aerospace control. Control systems on aircraft, therefore, must ensure the strict satisfaction of safety constraints, preferably with formal guarantees of safe behavior. This paper establishes the safety-critical control of fixed-wing aircraft in collision avoidance and geofencing tasks. A control framework is developed wherein a run-time assurance (RTA) system modulates the nominal flight controller of the aircraft whenever necessary to prevent it from colliding with other aircraft or crossing a boundary (geofence) in space. The RTA is formulated as a safety filter using control barrier functions (CBFs) with formal guarantees of safe behavior. CBFs are constructed and compared for a nonlinear kinematic fixed-wing aircraft model. The proposed CBF-based controllers showcase the capability of safely executing simultaneous collision avoidance and geofencing, as demonstrated by simulations on the kinematic model and a high-fidelity dynamical model.

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arXiv2024

Disturbance-Robust Backup Control Barrier Functions: Safety Under Uncertain Dynamics

Obtaining a controlled invariant set is crucial for safety-critical control with control barrier functions (CBFs) but is non-trivial for complex nonlinear systems and constraints. Backup control barrier functions allow such sets to be constructed online in a computationally tractable manner by examining the evolution (or flow) of the system under a known backup control law. However, for systems with unmodeled disturbances, this flow cannot be directly computed, making the current methods inadequate for assuring safety in these scenarios. To address this gap, we leverage bounds on the nominal and disturbed flow to compute a forward invariant set online by ensuring safety of an expanding norm ball tube centered around the nominal system evolution. We prove that this set results in robust control constraints which guarantee safety of the disturbed system via our Disturbance-Robust Backup Control Barrier Function (DR-bCBF) solution. The efficacy of the proposed framework is demonstrated in simulation, applied to a double integrator problem and a rigid body spacecraft rotation problem with rate constraints.

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arXiv2024

Rectified Control Barrier Functions for High-Order Safety Constraints

This paper presents a novel approach for synthesizing control barrier functions (CBFs) from high relative degree safety constraints: Rectified CBFs (ReCBFs). We begin by discussing the limitations of existing High-Order CBF approaches and how these can be overcome by incorporating an activation function into the CBF construction. We then provide a comparative analysis of our approach with related methods, such as CBF backstepping. Our results are presented first for safety constraints with relative degree two, then for mixed-input relative degree constraints, and finally for higher relative degrees. The theoretical developments are illustrated through simple running examples and an aircraft control problem.

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arXiv2024

Safety-Critical Controller Synthesis with Reduced-Order Models

Reduced-order models (ROMs) provide lower dimensional representations of complex systems, capturing their salient features while simplifying control design. Building on previous work, this paper presents an overarching framework for the integration of ROMs and control barrier functions, enabling the use of simplified models to construct safety-critical controllers while providing safety guarantees for complex full-order models. To achieve this, we formalize the connection between full and ROMs by defining projection mappings that relate the states and inputs of these models and leverage simulation functions to establish conditions under which safety guarantees may be transferred from a ROM to its corresponding full-order model. The efficacy of our framework is illustrated through simulation results on a drone and hardware demonstrations on ARCHER, a 3D hopping robot.

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arXiv2024

Safe and Stable Connected Cruise Control for Connected Automated Vehicles with Response Lag

Controlling connected automated vehicles (CAVs) via vehicle-to-everything (V2X) connectivity holds significant promise for improving fuel economy and traffic efficiency. However, to deploy CAVs and reap their benefits, their controllers must guarantee their safety. In this paper, we apply control barrier function (CBF) theory to investigate the safety of CAVs implementing connected cruise control (CCC). Specifically, we study how stability, connection architecture, and the CAV's response time impact the safety of CCC. Through safety and stability analyses, we derive stable and safe choices of control gains, and show that safe CAV operation requires plant and head-to-tail string stability in most cases. Furthermore, the reaction time of vehicles, which is represented as a first-order lag, has a detrimental effect on safety. We determine the critical value of this lag, above which safe CCC gains do not exist. To guarantee safety even with lag while preserving the benefits of CCC, we synthesize safety-critical CCC using CBFs. With the proposed safety-critical CCC, the CAV can leverage information from connected vehicles farther ahead to improve its safety. We evaluate this controller by numerical simulation using real traffic data.

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