Approximation-Free Control Barrier Functions for Prescribed-Time Reach-Avoid of Unknown Systems

Pushpak Jagtap; Shubham Sawarkar

arxiv: 2511.23022 · v2 · submitted 2025-11-28 · 📡 eess.SY · cs.RO· cs.SY· math.OC

Approximation-Free Control Barrier Functions for Prescribed-Time Reach-Avoid of Unknown Systems

Shubham Sawarkar , Pushpak Jagtap This is my paper

Pith reviewed 2026-05-17 04:34 UTC · model grok-4.3

classification 📡 eess.SY cs.ROcs.SYmath.OC

keywords control barrier functionsprescribed-time controlreach-avoidunknown dynamicsquadratic programmingdynamic obstaclessafety-critical systemsnonlinear control

0 comments

The pith

A virtual reference system with control barrier functions lets unknown nonlinear systems achieve prescribed-time reach-avoid without model learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a method for prescribed-time reach-avoid control of nonlinear systems whose dynamics are completely unknown and that must avoid moving obstacles. It first solves a control barrier function quadratic program on a simple virtual system to produce a reference trajectory that satisfies the reach-avoid conditions for suitably tightened time-varying sets. An approximation-free feedback law then keeps the true system inside a virtual confinement zone around that reference. A sympathetic reader would care because the construction requires neither online model identification nor uncertainty bound estimation, enabling immediate real-time use in dynamic environments.

Core claim

The construction guarantees real-time safety and prescribed-time target reachability under unknown dynamics and dynamic constraints without explicit model identification or offline precomputation by generating a safe reference on a virtual system via a CBF-QP and confining the true system to a Virtual Confinement Zone around this reference using an approximation-free feedback law.

What carries the argument

The Virtual Confinement Zone (VCZ) together with the approximation-free feedback law that confines the unknown real system to a neighborhood of the safe reference trajectory produced by a CBF-QP on the virtual system.

If this is right

Real-time safety is maintained with respect to time-varying obstacles for systems whose dynamics are never identified.
Prescribed-time convergence to the goal set occurs while dynamic constraints remain satisfied.
No online learning or uncertainty estimation is needed at any stage.
The approach supports immediate deployment in environments with moving obstacles without prior offline computation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same virtual-reference structure might extend naturally to systems with additional state or input constraints beyond reach-avoid.
It could reduce the computational burden in multi-agent settings where each agent uses its own virtual reference.
Testing the method on hardware with sensor noise would reveal how large the confinement zone must be in practice.

Load-bearing premise

That an approximation-free feedback law exists which can confine any unknown nonlinear system to the Virtual Confinement Zone around the virtual reference while preserving the prescribed-time properties.

What would settle it

A simulation or experiment in which the real system exits the Virtual Confinement Zone or misses the target set at the prescribed time despite the feedback law being applied to truly unknown dynamics and moving obstacles.

Figures

Figures reproduced from arXiv: 2511.23022 by Pushpak Jagtap, Shubham Sawarkar.

**Figure 1.** Figure 1: Control Flowchart (1) Virtual control design: a CBF-QP-based controller that navigates the VCZ center. (2) Confinement control design: a separate controller maintains the system state within the evolving VCZ. Step 1: Virtual Control Design using CBF-QP over VCZ dynamics Consider a prescribed-time reach-avoid problem defined in Problem 1, where unsafe region U(t) is defined as the union of d − 1 moving obst… view at source ↗

**Figure 2.** Figure 2: (a) Trajectory plot in state space for PT-RA over [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

read the original abstract

We study the prescribed-time reach-avoid (PT-RA) control problem for nonlinear systems with unknown dynamics operating in environments with moving obstacles. Unlike robust or learning based Control Barrier Function (CBF) methods, the proposed framework requires neither online model learning nor uncertainty bound estimation. A CBF-based Quadratic Program (CBF-QP) is solved on a simple virtual system to generate a safe reference satisfying PT-RA conditions with respect to time-varying, tightened obstacle and goal sets. The true system is confined to a Virtual Confinement Zone (VCZ) around this reference using an approximation-free feedback law. This construction guarantees real-time safety and prescribed-time target reachability under unknown dynamics and dynamic constraints without explicit model identification or offline precomputation. Simulation results illustrate reliable dynamic obstacle avoidance and timely convergence to the target set.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper sketches a model-free route to prescribed-time reach-avoid via a virtual CBF-QP plus confinement to a VCZ, but the existence of the approximation-free law for arbitrary unknown dynamics is asserted without visible derivation or bounds.

read the letter

The one thing to take away is that the authors avoid online learning or uncertainty estimation by solving the CBF-QP on a simple virtual system and then using a feedback law to keep the real trajectory inside a Virtual Confinement Zone around the virtual reference. This is meant to transfer the prescribed-time safety and reachability properties to the unknown true system with moving obstacles. The construction is presented as independent of any fitted model, which is the main departure from robust or learning-based CBF work. What they do reasonably well is frame the practical problem clearly and contrast it with methods that require bounds or adaptation. The virtual reference plus tightened sets is a clean way to handle dynamic constraints without precomputing everything offline. The soft spot sits right at the confinement step. The abstract states that an approximation-free law confines any unknown nonlinear system to the VCZ while preserving the time guarantees, yet the text gives no derivation of the law, no error dynamics analysis, and no conditions under which the radius stays valid. When the true vector field can grow arbitrarily or is not control-affine, it is not obvious how a fixed feedback without access to f or g can dominate the mismatch. That gap is the least secure part of the argument. This paper is for control researchers working on safety-critical tasks with uncertain dynamics and strict timing, such as robotics in changing environments. A reader already familiar with CBF-QP formulations will see the virtual-system trick quickly and may find the idea worth testing in simulation. It deserves a serious referee because the problem statement is relevant and the claimed separation of virtual planning from real-system confinement is distinct, even though the central existence claim needs the full proofs and any supporting lemmas to be checked.

Referee Report

1 major / 2 minor

Summary. The paper claims to solve the prescribed-time reach-avoid (PT-RA) problem for nonlinear systems with unknown dynamics and moving obstacles. A CBF-QP is solved on a virtual system to produce a safe reference trajectory satisfying PT-RA conditions relative to time-varying tightened obstacle and goal sets. The true system is then confined to a Virtual Confinement Zone (VCZ) around this reference by an approximation-free feedback law. The construction is asserted to guarantee real-time safety and prescribed-time target reachability without model identification, online learning, uncertainty bounds, or offline precomputation. Simulation results are presented to illustrate dynamic obstacle avoidance and timely convergence.

Significance. If the central claims hold, the result would be significant for safe control of unknown systems in dynamic environments, as it avoids the computational and modeling requirements common to robust or learning-based CBF approaches while incorporating prescribed-time convergence. The virtual-system reference plus VCZ confinement is a conceptually clean way to separate reference generation from the unknown plant. Credit is due for the attempt to produce an approximation-free method with explicit PT-RA guarantees and for providing simulation evidence of practical behavior.

major comments (1)

The central construction (existence and design of the approximation-free confinement law for arbitrary unknown dynamics) is asserted without visible derivation steps or error analysis. The error dynamics between the true state and the virtual reference are completely unknown; no argument is given showing how a feedback law without access to f, g or uncertainty bounds can dominate destabilizing or growing terms to enforce strict confinement to the VCZ up to the user-specified time T. This is load-bearing for both the safety claim (via the tightened sets) and the prescribed-time reachability claim.

minor comments (2)

Clarify the precise definition of the VCZ radius and the tightened sets (including how the tightening margin is chosen) in the preliminary or problem-statement section.
The abstract and introduction would benefit from an explicit statement of the system class (control-affine or not) and any standing assumptions on the unknown vector fields.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need for greater clarity on the central technical construction. We agree that the approximation-free confinement law and its guarantees require a more explicit derivation and error analysis in the manuscript. We will revise the paper to address this.

read point-by-point responses

Referee: The central construction (existence and design of the approximation-free confinement law for arbitrary unknown dynamics) is asserted without visible derivation steps or error analysis. The error dynamics between the true state and the virtual reference are completely unknown; no argument is given showing how a feedback law without access to f, g or uncertainty bounds can dominate destabilizing or growing terms to enforce strict confinement to the VCZ up to the user-specified time T. This is load-bearing for both the safety claim (via the tightened sets) and the prescribed-time reachability claim.

Authors: We acknowledge that the current presentation condenses the construction of the approximation-free feedback law and the associated confinement argument. In the revised manuscript we will add a dedicated subsection that derives the law explicitly. The law takes the form of a time-varying, high-gain feedback that is independent of f and g; its gain is scheduled to enforce finite-time entry into the VCZ and invariance thereafter. The proof proceeds by showing that the closed-loop error norm satisfies a differential inequality whose solution reaches and remains inside the VCZ radius before the prescribed time T, using only the definition of the VCZ and the fact that the virtual reference already satisfies the tightened PT-RA conditions. While the referee correctly notes that no a-priori uncertainty bounds are assumed, the time-varying gain is constructed to grow sufficiently fast to dominate any continuous (but unknown) vector field on the compact time interval [0,T]. We will include the full step-by-step error analysis and the explicit gain schedule so that the load-bearing claims for safety and reachability become fully traceable. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation separates virtual reference generation from independent confinement step

full rationale

The paper's chain proceeds by first solving a CBF-QP on an independent virtual system to produce a safe reference trajectory satisfying PT-RA on tightened sets, then applying a separate approximation-free feedback law to keep the true state inside the VCZ around that reference. This structure does not reduce any claimed guarantee to a fitted parameter renamed as prediction, a self-defined quantity, or a load-bearing self-citation whose validity is presupposed by the present work. The virtual-system step and the confinement law are presented as distinct constructions, each with its own stated assumptions, so the overall result remains self-contained against external benchmarks rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The central guarantee rests on the existence of a suitable confinement feedback law for arbitrary unknown dynamics and on the ability to tighten obstacle and goal sets so that the virtual reference remains feasible.

axioms (1)

domain assumption There exists an approximation-free feedback law capable of confining the unknown true system to the Virtual Confinement Zone while preserving the prescribed-time properties of the reference.
This premise is required for the safety and timing transfer from virtual to real system and is not derived in the abstract.

invented entities (2)

Virtual Confinement Zone (VCZ) no independent evidence
purpose: A buffer region around the virtual reference that the true system is forced to remain inside.
New construct introduced to bridge the virtual safe reference to the unknown true dynamics.
Tightened obstacle and goal sets no independent evidence
purpose: Time-varying sets used in the virtual CBF-QP that account for the confinement margin.
Invented to make the virtual planning conservative enough for the real system.

pith-pipeline@v0.9.0 · 5446 in / 1328 out tokens · 36926 ms · 2026-05-17T04:34:29.566397+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel / Jcost_pos_of_ne_one echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

u := −k ζ(ê) ϕ(e) where ζ(ê) := ln((1+ê)/(1−ê)) … V(e) := ζ²(ê) … uniformly ultimately bounded on B°(0,rc)
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative refines

?

refines
Relation between the paper passage and the cited Recognition theorem.

Virtual Confinement Zone C(t) := B°(c(t), rc) … true state confined inside VCZ inherits PT-RA

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

[1]

Taylor, Chaozhe R

Anil Alan, Andrew J. Taylor, Chaozhe R. He, Aaron D. Ames, and Gábor Orosz. Control barrier functions and input-to-state safety with application to automated vehicles.IEEE Transactions on Control Systems Technology, 31(6):2744–2759, 2023

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[2]

Ames, Samuel Coogan, Magnus Egerstedt, Gennaro Notomista, Koushil Sreenath, and Paulo Tabuada

Aaron D. Ames, Samuel Coogan, Magnus Egerstedt, Gennaro Notomista, Koushil Sreenath, and Paulo Tabuada. Control barrier functions: Theory and applications. In18th European Control Conference (ECC), pages 3420– 3431, 2019. 9 APREPRINT- DECEMBER1, 2025

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Bechlioulis and George A

Charalampos P. Bechlioulis and George A. Rovithakis. Robust adaptive control of feedback linearizable mimo nonlinear systems with prescribed performance.IEEE Transactions on Automatic Control, 53(9):2090–2099, 2008

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Thomas Berger, Huy Hoàng Lê, and Timo Reis. Funnel control for nonlinear systems with known strict relative degree.Automatica, 87:345–357, 2018

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Robust control barrier functions with sector-bounded uncertainties

Jyot Buch, Shih-Chi Liao, and Peter Seiler. Robust control barrier functions with sector-bounded uncertainties. IEEE Control Systems Letters, 6:1994–1999, 2022

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Cohen, Tamas G

Max H. Cohen, Tamas G. Molnar, and Aaron D. Ames. Safety-critical control for autonomous systems: Control barrier functions via reduced-order models.Annual Reviews in Control, 57:100947, 2024

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Spatiotemporal tubes for temporal reach-avoid-stay tasks in unknown systems.IEEE Transactions on Automatic Control, pages 1–8, 2025

Ratnangshu Das, Ahan Basu, and Pushpak Jagtap. Spatiotemporal tubes for temporal reach-avoid-stay tasks in unknown systems.IEEE Transactions on Automatic Control, pages 1–8, 2025

work page 2025
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Prescribed-time reach-avoid-stay specifications for unknown systems: A spatiotemporal tubes approach.IEEE Control Systems Letters, 8:946–951, 2024

Ratnangshu Das and Pushpak Jagtap. Prescribed-time reach-avoid-stay specifications for unknown systems: A spatiotemporal tubes approach.IEEE Control Systems Letters, 8:946–951, 2024

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Pappas, and Majid Zamani

Pushpak Jagtap, George J. Pappas, and Majid Zamani. Control barrier functions for unknown nonlinear systems using Gaussian processes. In59th IEEE Conference on Decision and Control (CDC), pages 3699–3704, 2020

work page 2020
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Formal synthesis of stochastic systems via control barrier certificates.IEEE Transactions on Automatic Control, 66(7):3097–3110, 2020

Pushpak Jagtap, Sadegh Soudjani, and Majid Zamani. Formal synthesis of stochastic systems via control barrier certificates.IEEE Transactions on Automatic Control, 66(7):3097–3110, 2020

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Robust control barrier functions for constrained stabilization of nonlinear systems.Automatica, 96:359–367, 2018

Mrdjan Jankovic. Robust control barrier functions for constrained stabilization of nonlinear systems.Automatica, 96:359–367, 2018

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Dimarogonas

Lars Lindemann and Dimos V . Dimarogonas. Control barrier functions for signal temporal logic tasks.IEEE Control Systems Letters, 3(1):96–101, 2019

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Bechlioulis, and Dimos V

Farhad Mehdifar, Charalampos P. Bechlioulis, and Dimos V . Dimarogonas. Funnel control under hard and soft output constraints. InIEEE 61st Conference on Decision and Control (CDC), pages 4473–4478, 2022

work page 2022
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Mitchell, A.M

I.M. Mitchell, A.M. Bayen, and C.J. Tomlin. A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games.IEEE Transactions on Automatic Control, 50(7):947–957, 2005

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Funnel-based reward shaping for signal temporal logic tasks in reinforcement learning.IEEE Robotics and Automation Letters, 9(2):1373–1379, 2024

Naman Saxena, Sandeep Gorantla, and Pushpak Jagtap. Funnel-based reward shaping for signal temporal logic tasks in reinforcement learning.IEEE Robotics and Automation Letters, 9(2):1373–1379, 2024

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Control barrier functions with unmodeled input dynamics using integral quadratic constraints.IEEE Control Systems Letters, 6:1664–1669, 2022

Peter Seiler, Mrdjan Jankovic, and Erik Hellstrom. Control barrier functions with unmodeled input dynamics using integral quadratic constraints.IEEE Control Systems Letters, 6:1664–1669, 2022

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Paulo Tabuada.Verification and control of hybrid systems: a symbolic approach. Springer Science & Business Media, 2009

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Robust constrained stabilization control using control Lyapunov and control barrier function in the presence of measurement noises

Rin Takano and Masaki Yamakita. Robust constrained stabilization control using control Lyapunov and control barrier function in the presence of measurement noises. InIEEE Conference on Control Technology and Applications (CCTA), pages 300–305, 2018

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Control barrier functions in dynamic uavs for kinematic obstacle avoidance: A collision cone approach

Manan Tayal, Rajpal Singh, Jishnu Keshavan, and Shishir Kolathaya. Control barrier functions in dynamic uavs for kinematic obstacle avoidance: A collision cone approach. In2024 American Control Conference (ACC), pages 3722–3727, July 2024

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Wabersich, Andrew J

Kim P. Wabersich, Andrew J. Taylor, Jason J. Choi, Koushil Sreenath, Claire J. Tomlin, Aaron D. Ames, and Melanie N. Zeilinger. Data-driven safety filters: Hamilton-jacobi reachability, control barrier functions, and predictive methods for uncertain systems.IEEE Control Systems Magazine, 43(5):137–177, 2023

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Grizzle, and Aaron D

Xiangru Xu, Paulo Tabuada, Jessy W. Grizzle, and Aaron D. Ames. Robustness of control barrier functions for safety critical control.IFAC-PapersOnLine, 48(27):54–61, 2015. 10 APREPRINT- DECEMBER1, 2025 A Proof of Lemma 2 Proof.The obstacle avoidance CBF condition from (7) can be written as: aj(c, t)⊤uc ≥ρ j(c, t), j= 1,2, . . . , d−1, witha j(c, t) = 2g c(...

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[1] [1]

Taylor, Chaozhe R

Anil Alan, Andrew J. Taylor, Chaozhe R. He, Aaron D. Ames, and Gábor Orosz. Control barrier functions and input-to-state safety with application to automated vehicles.IEEE Transactions on Control Systems Technology, 31(6):2744–2759, 2023

work page 2023

[2] [2]

Ames, Samuel Coogan, Magnus Egerstedt, Gennaro Notomista, Koushil Sreenath, and Paulo Tabuada

Aaron D. Ames, Samuel Coogan, Magnus Egerstedt, Gennaro Notomista, Koushil Sreenath, and Paulo Tabuada. Control barrier functions: Theory and applications. In18th European Control Conference (ECC), pages 3420– 3431, 2019. 9 APREPRINT- DECEMBER1, 2025

work page 2019

[3] [3]

Bechlioulis and George A

Charalampos P. Bechlioulis and George A. Rovithakis. Robust adaptive control of feedback linearizable mimo nonlinear systems with prescribed performance.IEEE Transactions on Automatic Control, 53(9):2090–2099, 2008

work page 2090

[4] [4]

Thomas Berger, Achim Ilchmann, and Eugene P. Ryan. Funnel control of nonlinear systems.Mathematics of Control, Signals, and Systems, 33(1):151–194, 2021

work page 2021

[5] [5]

Funnel control for nonlinear systems with known strict relative degree.Automatica, 87:345–357, 2018

Thomas Berger, Huy Hoàng Lê, and Timo Reis. Funnel control for nonlinear systems with known strict relative degree.Automatica, 87:345–357, 2018

work page 2018

[6] [6]

Robust control barrier functions with sector-bounded uncertainties

Jyot Buch, Shih-Chi Liao, and Peter Seiler. Robust control barrier functions with sector-bounded uncertainties. IEEE Control Systems Letters, 6:1994–1999, 2022

work page 1994

[7] [7]

Cohen, Tamas G

Max H. Cohen, Tamas G. Molnar, and Aaron D. Ames. Safety-critical control for autonomous systems: Control barrier functions via reduced-order models.Annual Reviews in Control, 57:100947, 2024

work page 2024

[8] [8]

Spatiotemporal tubes for temporal reach-avoid-stay tasks in unknown systems.IEEE Transactions on Automatic Control, pages 1–8, 2025

Ratnangshu Das, Ahan Basu, and Pushpak Jagtap. Spatiotemporal tubes for temporal reach-avoid-stay tasks in unknown systems.IEEE Transactions on Automatic Control, pages 1–8, 2025

work page 2025

[9] [9]

Prescribed-time reach-avoid-stay specifications for unknown systems: A spatiotemporal tubes approach.IEEE Control Systems Letters, 8:946–951, 2024

Ratnangshu Das and Pushpak Jagtap. Prescribed-time reach-avoid-stay specifications for unknown systems: A spatiotemporal tubes approach.IEEE Control Systems Letters, 8:946–951, 2024

work page 2024

[10] [10]

Pappas, and Majid Zamani

Pushpak Jagtap, George J. Pappas, and Majid Zamani. Control barrier functions for unknown nonlinear systems using Gaussian processes. In59th IEEE Conference on Decision and Control (CDC), pages 3699–3704, 2020

work page 2020

[11] [11]

Formal synthesis of stochastic systems via control barrier certificates.IEEE Transactions on Automatic Control, 66(7):3097–3110, 2020

Pushpak Jagtap, Sadegh Soudjani, and Majid Zamani. Formal synthesis of stochastic systems via control barrier certificates.IEEE Transactions on Automatic Control, 66(7):3097–3110, 2020

work page 2020

[12] [12]

Robust control barrier functions for constrained stabilization of nonlinear systems.Automatica, 96:359–367, 2018

Mrdjan Jankovic. Robust control barrier functions for constrained stabilization of nonlinear systems.Automatica, 96:359–367, 2018

work page 2018

[13] [13]

Khalil.Nonlinear Systems

Hassan K. Khalil.Nonlinear Systems. Prentice Hall, Upper Saddle River, NJ, 3rd edition, 2002

work page 2002

[14] [14]

Shishir Kolathaya and Aaron D. Ames. Input-to-state safety with control barrier functions.IEEE Control Systems Letters, 3(1):108–113, 2019

work page 2019

[15] [15]

Dimarogonas

Lars Lindemann and Dimos V . Dimarogonas. Control barrier functions for signal temporal logic tasks.IEEE Control Systems Letters, 3(1):96–101, 2019

work page 2019

[16] [16]

Bechlioulis, and Dimos V

Farhad Mehdifar, Charalampos P. Bechlioulis, and Dimos V . Dimarogonas. Funnel control under hard and soft output constraints. InIEEE 61st Conference on Decision and Control (CDC), pages 4473–4478, 2022

work page 2022

[17] [17]

Mitchell, A.M

I.M. Mitchell, A.M. Bayen, and C.J. Tomlin. A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games.IEEE Transactions on Automatic Control, 50(7):947–957, 2005

work page 2005

[18] [18]

Funnel-based reward shaping for signal temporal logic tasks in reinforcement learning.IEEE Robotics and Automation Letters, 9(2):1373–1379, 2024

Naman Saxena, Sandeep Gorantla, and Pushpak Jagtap. Funnel-based reward shaping for signal temporal logic tasks in reinforcement learning.IEEE Robotics and Automation Letters, 9(2):1373–1379, 2024

work page 2024

[19] [19]

Control barrier functions with unmodeled input dynamics using integral quadratic constraints.IEEE Control Systems Letters, 6:1664–1669, 2022

Peter Seiler, Mrdjan Jankovic, and Erik Hellstrom. Control barrier functions with unmodeled input dynamics using integral quadratic constraints.IEEE Control Systems Letters, 6:1664–1669, 2022

work page 2022

[20] [20]

Springer Science & Business Media, 2009

Paulo Tabuada.Verification and control of hybrid systems: a symbolic approach. Springer Science & Business Media, 2009

work page 2009

[21] [21]

Robust constrained stabilization control using control Lyapunov and control barrier function in the presence of measurement noises

Rin Takano and Masaki Yamakita. Robust constrained stabilization control using control Lyapunov and control barrier function in the presence of measurement noises. InIEEE Conference on Control Technology and Applications (CCTA), pages 300–305, 2018

work page 2018

[22] [22]

Control barrier functions in dynamic uavs for kinematic obstacle avoidance: A collision cone approach

Manan Tayal, Rajpal Singh, Jishnu Keshavan, and Shishir Kolathaya. Control barrier functions in dynamic uavs for kinematic obstacle avoidance: A collision cone approach. In2024 American Control Conference (ACC), pages 3722–3727, July 2024

work page 2024

[23] [23]

Wabersich, Andrew J

Kim P. Wabersich, Andrew J. Taylor, Jason J. Choi, Koushil Sreenath, Claire J. Tomlin, Aaron D. Ames, and Melanie N. Zeilinger. Data-driven safety filters: Hamilton-jacobi reachability, control barrier functions, and predictive methods for uncertain systems.IEEE Control Systems Magazine, 43(5):137–177, 2023

work page 2023

[24] [24]

Grizzle, and Aaron D

Xiangru Xu, Paulo Tabuada, Jessy W. Grizzle, and Aaron D. Ames. Robustness of control barrier functions for safety critical control.IFAC-PapersOnLine, 48(27):54–61, 2015. 10 APREPRINT- DECEMBER1, 2025 A Proof of Lemma 2 Proof.The obstacle avoidance CBF condition from (7) can be written as: aj(c, t)⊤uc ≥ρ j(c, t), j= 1,2, . . . , d−1, witha j(c, t) = 2g c(...

work page 2015