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Predictive Synthesis of Control Barrier Functions and its Application to Time-Varying Constraints

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A finite-horizon optimal control problem, solved pointwise, produces a control barrier function that remains valid when constraints change over time, without recomputation.

desk verdict A promising predictive CBF synthesis with a real gap in the proof of the main theorem: Step 1 of Theorem 6 needs right-continuity of the optimal control that isn't assumed. read the letter →

arxiv 2504.15830 v1 pith:L3CC35FL submitted 2025-04-22 eess.SY cs.SYmath.OC

Adrian Wiltz , Dimos V. Dimarogonas This is my paper · ORCID
classification eess.SYcs.SYmath.OC
keywords controlbarrierfunctionspredictiveCBFsynthesistime-varyingconstraintsDiniderivativeHamilton-Jacobireachabilityfinite-horizonoptimalshiftableinput
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to prove that a control barrier function can be synthesized pointwise as the value of a finite-horizon optimal control problem, and that this value function is itself a CBF in the Dini sense on a domain larger than its safe set. The payoff is reusability: because the CBF is defined through a prediction horizon rather than a fixed constraint shape, adding a time-varying offset within a prescribed bound produces another valid CBF, so moving or expanding constraints do not force a full recomputation. The authors also give an explicit construction of the extended class K function alpha that appears in the CBF inequality, and show that alpha can instead be chosen directly as a design parameter. If the construction holds, safety filters can be built for systems with input constraints and weak controllability, without needing a nominal backup controller.

What carries the argument

The central object is the finite-horizon value function HT defined in (8): HT(x0) = max over input trajectories in U[0,T] of min over t in [0,T] of h(x(t)) - gamma t, with the state trajectory required to hit the known set F at some time within the horizon. The machinery consists of two complementary bounds on its Dini derivative: near the boundary of the safe set the gamma penalty forces an asymmetric ascend of at least gamma along the optimal trajectory, while inside the safe set a Lipschitz bound LM bounds the worst possible descent; these are combined in (20) into an explicit extended class K function alpha so that sup_u dHT(x; f(x,u)) >= -alpha(HT(x)) holds on all of D. The same structure is what makes HT shiftable in the sense of [55], since the ascend margin near the boundary tolerates the addition of a bounded time-varying offset.

What would settle it

Compute HT from (8) for a system satisfying Assumptions 1 and 2 in which the finite-horizon value is nonrobust in the sense of the examples cited in [64]; if on a fine grid of D there is any state x where the supremum over u in U of the Dini derivative dHT(x; f(x,u)) is strictly less than -alpha(HT(x)), or where HT is visibly discontinuous, then the claimed certificate in (10) is not delivered by the synthesis.

Watch

Extended reading notes

Core claim

The central claim, formalized as Theorem 6, is that for a Lipschitz constraint function h and a known subset F of an (unknown) forward control invariant set V, the function HT(x0) = max over input trajectories of the minimum over the horizon of h(x(t)) - gamma t, subject to reaching F within time T, is a control barrier function in the Dini sense on the whole domain D. This holds when Assumptions 1 and 2 are satisfied, T >= tau, gamma < delta/T, f is bounded on the safe set, and HT happens to be locally Lipschitz. The negative gamma-t term is what makes the proof work: along the optimal predictive trajectory the value strictly increases at rate at least gamma on a neighborhood of the safe set's boundary, and the boundedness of f plus Lipschitz continuity bounds any possible decrease away from the boundary. Those two bounds are glued into an explicit extended class K function alpha in (20), and a modified synthesis (29) lets alpha itself be chosen by the designer. Since the CBF is defined on D rather than only on its zero super-level set, HT is shiftable: HT + lambda(t) remains a CBF for any time-varying lambda satisfying (36), which is how the method handles time-varying constraints.

Load-bearing premise

The load-bearing premise is that the value function HT is locally Lipschitz continuous; the paper assumes this in Theorem 6 and only verifies it numerically after the fact, noting in Remark 3 that finite-horizon optimal control values can be nonrobust.

Editorial extensions

If this is right

  • If the central theorem is correct, one CBF computation for a static constraint automatically yields valid CBFs for a whole family of time-varying constraints, through HT(x) + lambda(t) with lambda obeying the explicit rate condition (36).
  • The explicit class K function means the safety margin encoded in the CBF inequality is known, and in the alpha-based version (29) it becomes a direct design parameter rather than an implicit outcome of the computation.
  • Because the method needs no nominal control law and only a known subset F of an invariant set, it applies to non-locally-controllable and nonholonomic systems such as the bicycle and unicycle examples, and automatically accounts for input constraints.
  • Longer prediction horizons enlarge the guaranteed safe sets C_lambda,T, so the horizon T can be traded off against the size of the region in which safety is certified.
  • Pointwise evaluation means the CBF does not have to be gridded over the whole domain; this is what allows the method to be parallelized and to be combined with symmetry reduction in the follow-up work.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The pointwise evaluation property suggests a natural testable extension: fit the computed values of HT with a neural network or another regressor and certify the learned function by checking the Dini condition on a grid; the paper only uses linear interpolation in its examples.
  • The gamma-based ascend margin near the boundary could plausibly confer a form of input robustness: disturbances smaller than the margin would not immediately destroy the CBF inequality, though the paper does not analyze robustness to model error.
  • The local Lipschitz assumption on HT is the soft spot; a useful extension would be to identify structural conditions on f and U beyond the nonrobust examples cited in [64] under which this regularity is guaranteed a priori rather than verified numerically.
  • Since HT is computed only on a subset and then interpolated, the actual safety guarantee for interpolated points depends on the interpolation error; establishing a Lipschitz bound on HT would let the interpolation error be bounded and the filter made certifiably safe on the full grid-free domain.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes a method for synthesizing Control Barrier Functions (CBFs) by solving a finite-horizon max-min optimal control problem. The resulting function HT is claimed to be a CBF in the Dini sense on a domain D that may be larger than its zero superlevel set, with an explicit extended class Ke function alpha. The method is designed to handle input constraints, to provide pointwise values of the CBF without computing it globally, and to be robust to time-varying constraints by yielding a shiftable CBF. The paper includes three variants of the construction, implementation remarks with a discrete-time approximation, and simulations for single/double integrators, a kinematic bicycle, and a unicycle.

Significance. If the main theorem is correct, the paper offers a useful addition to the CBF synthesis literature: it avoids a nominal control law, produces an explicit alpha, allows domain D larger than C, and enables time-varying constraint handling through shiftability. The pointwise computability and the accompanying open-source implementation are concrete strengths. However, the central proof of Theorem 6 has a load-bearing gap in the passage from a finite-horizon growth inequality to the infinitesimal Dini-derivative condition, and a second gap in the treatment of the boundedness assumption. These issues affect the formal certificate of safety for the synthesized function as currently written. The overall idea is promising, but the theoretical core needs repair before the claims can be accepted.

major comments (3)
  1. [Section IV.A, Theorem 6, Step 1, Eq. (18)-(19)] The proof does not justify the transition from the finite-horizon inequality (17) to the infinitesimal Dini-derivative inequality (19d). Equation (18) relies on the expansion phi(sigma;x0,u*) = x0 + sigma f(x0,u*(0)) + O(sigma^2), but u* is only bounded and measurable, and no right-continuity (or right Lebesgue point) of u* at 0 is assumed. The remainder integral of f(phi(s),u*(s)) - f(x0,u*(0)) is then generally O(sigma), not O(sigma^2), so equality (18c) fails even when HT is locally Lipschitz. Consequently the CBF inequality (10) is not established on the 'blue region' outside C, which is the critical part of the domain for the certificate. In addition, (17) is stated for the fixed epsilon chosen in (11); taking the limit sigma->0 in (19d) requires the same inequality for all sufficiently small sigma, which the proof does not show.
  2. [Section IV.A, Theorem 6, Step 2, Eq. (22)-(23)] The boundedness assumption on f is not sufficient for the estimate in (22). The assumption 'for all x in C there exists u in U such that ||f(x,u)|| <= M' is existential in x and does not imply that the chosen constant input u at x0 satisfies ||f(phi(s;x0,u),u)|| <= M for s in [0,sigma], especially if the trajectory leaves C. The proof needs f to be bounded on a neighborhood of C (or on C x U with C compact and U compact) and the input chosen so that the bound holds along the trajectory. As written, the lower bound (23) and hence the conclusion (24d) for the 'green region' are not proven.
  3. [Definition 1 and Theorem 6] Definition 1 requires the zero superlevel set C = {x | HT(x) >= 0} to be compact, but the paper does not prove compactness of C and does not include it as an explicit assumption. In the numerical examples, H is the complement of a disk and is unbounded, so compactness is not automatic. Without an added compactness or bounded-domain assumption, HT does not formally satisfy Definition 1 as a CBF.
minor comments (4)
  1. [Section IV.A, Eq. (17)] The sentence 'for all t' in [0,T]' after Eq. (17) is confusing because (17) contains no such parameter; it should be clarified that the argument can be repeated for every smaller positive epsilon' if the infinitesimal passage is intended.
  2. [Section IV.A, Remark 3] The local Lipschitz continuity of HT is assumed as a premise and is only checked numerically a posteriori; the paper should state more prominently that Theorem 6 is a verification theorem conditional on this regularity, not a construction that guarantees it.
  3. [Section V.B, Proposition 10] Proposition 10 relies on [55, Theorem 4] and assumes differentiability of HT; the paper should note explicitly that the time-varying CBF claim is not self-contained and that differentiability is not verified for the numerical examples.
  4. [Section VI.B, Eq. (41) and Algorithm 1] The notation for the p-norm approximation is unclear: 'p " 0' appears to be a typo, and the text should state that p is chosen sufficiently large (p >> 0). Additionally, the constant h-tilde requires min_{x in D} h(x) to exist and be finite, which needs an explicit boundedness assumption on D and h.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the CBF property of HT is derived from the defining OCP; self-citations to [56] and [55] are used as external lemmas, not as the source of the central claim.

full rationale

The central claim (Theorem 6) is derived, not assumed: HT is defined by the finite-horizon OCP (8), and the proof establishes the Dini inequality (10) by combining the suboptimality argument (16) with the Dini-derivative bridge (18) and the Lipschitz bound (23). No parameter is fitted to a subset of data and then renamed a prediction; the only free parameters (gamma, T, epsilon) are chosen a priori and control the derived bound. The paper's self-citations are Proposition 4 from [56] (existence of finite tau) and Proposition 10 from [55] (shiftability). Both are published prior results with stated assumptions that do not include the present theorem, so they serve as external lemmas rather than a self-referential chain; the current paper proves the actual CBF property of HT on its own. The explicit construction of alpha in (20) and the saturation result are post-hoc choices that satisfy the derived bounds (gamma and LM), so they do not smuggle the conclusion into the premise. The principal technical weakness is not circularity: eq. (18) requires a Taylor expansion phi(sigma)=x0+sigma f(x0,u*(0))+O(sigma^2), which is not justified under the stated bounded-measurable input assumption, and Remark 3 concedes that local Lipschitz continuity is only verified numerically. These are correctness gaps, not reductions of the prediction to the input. Accordingly, no circular step can be exhibited with a specific equation-to-equation reduction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central construction relies on a handful of explicit design parameters (gamma, delta, T) and structural assumptions about a known invariant subset and controllability. No new physical entities are introduced. The value function HT is constructed, not postulated.

free parameters (3)
  • gamma (ascend rate) = Table I: 2 for single integrators and bicycle, 1 for double integrator
    Positive discount/ascend rate in OCP (8); user-chosen subject to gamma < delta/T. It sets the minimal ascend in Step 1 of Theorem 6 and shapes the class-K function alpha. Not fitted to data, but a free design parameter.
  • delta (constraint margin) = Table I: 1 (single integrators), 5 (double integrator), 9 and 4 (bicycles), 4 (unicycle)
    Assumption 1 margin: h(x) >= delta on the invariant set V. Must be known or estimated a priori; enters the condition gamma < delta/T and the threshold delta - gamma(epsilon+1)T.
  • prediction horizon T = Table I: 10, 12, 12, 10, 10
    Finite horizon in the OCP, chosen T >= tau where tau bounds the minimal time to reach F. Larger T enlarges the safe set (Proposition 9) but increases computation.
assumptions (5)
  • domain assumption Assumption 1: There exists a forward control invariant set V subset H with h(x) >= delta on V, and a known subset F subset V.
    Section III.A. The whole synthesis assumes such F and delta are available; Example 1 constructs F for a bicycle.
  • domain assumption Assumption 2: The system is controllable to F in finite time (either controllability on closure of F^c or reachability of F from every state in D\F).
    Section III.B. Ensures tau is finite and OCP (8) is feasible.
  • domain assumption The value function HT is locally Lipschitz continuous and f is bounded on C.
    Theorems 6 and 8, Section IV. Local Lipschitz is used in (18) and in Step 2; the paper notes it can only be verified after computation (Remark 3).
  • standard math h and f are Lipschitz continuous; forward completeness of solutions.
    Section II, standing assumptions.
  • standard math Comparison Lemma and standard properties of class K and extended class Ke functions.
    Used in Theorem 1 and the construction of alpha.

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Cite this review

Pith. "Pith review of Predictive Synthesis of Control Barrier Functions and its Application to Time-Varying Constraints." pith.science (2026). https://pith.science/paper/L3CC35FL

@misc{pith2026250415830,
  author       = {Pith},
  title        = {Pith review of: Predictive Synthesis of Control Barrier Functions and its Application to Time-Varying Constraints},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L3CC35FL}},
  note         = {Machine review of arXiv:2504.15830}
}
read the original abstract

This paper presents a systematic method for synthesizing a Control Barrier Function (CBF) that encodes predictive information into a CBF. Unlike other methods, the synthesized CBF can account for changes and time-variations in the constraints even when constructed for time-invariant constraints. This avoids recomputing the CBF when the constraint specifications change. The method provides an explicit characterization of the extended class K function {\alpha} that determines the dynamic properties of the CBF, and {\alpha} can even be explicitly chosen as a design parameter in the controller synthesis. The resulting CBF further accounts for input constraints, and its values can be determined at any point without having to compute the CBF over the entire domain. The synthesis method is based on a finite horizon optimal control problem inspired by Hamilton-Jacobi reachability analysis and does not rely on a nominal control law. The synthesized CBF is time-invariant if the constraints are. The method poses mild assumptions on the controllability of the dynamic system and assumes the knowledge of at least a subset of some control invariant set. The paper provides a detailed analysis of the properties of the synthesized CBF, including its application to time-varying constraints. A simulation study applies the proposed approach to various dynamic systems in the presence of time-varying constraints. The paper is accompanied by an online available parallelized implementation of the proposed synthesis method.

Figures

Figures reproduced from arXiv: 2504.15830 by the authors.

Figure 1
Figure 1. Illustration of Assumption 1. β ζ ψ L C v (a) V y x R hpxq “ δ F Hc hpxq “ δ ` 2R (b) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Kinematic bicycle model: (a) schematic sketch; (b) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Relation of the defined sets. The particular shapes of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Schematic sketch of the extended class Ke function α. for all x0 with HT px0q ď δ ´ γpε ` 1qT where α is some suitable extended class Ke function that we choose as αpζq “ # α1pζq ζ ě 0 α2pζq ζ ă 0 (20) such that ´γ ď αpζq (21) holds. To satisfy condition (21), we choos…
Figure 6
Figure 6. Figure 6: Simulation results for single and double integrators: [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 8
Figure 8. Figure 8: Simulation results for the kinematic unicycle model. [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 7
Figure 7. Figure 7: Simulation results for the kinematic bicycle model: the [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

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Works this paper leans on

66 extracted references · 46 canonical work pages · cited by 1 Pith paper

  1. [1]

    Constructive safety using control barrier functions,

    P. Wieland and F. Allgöwer, “Constructive safety using control barrier functions,” IFAC Proceedings Volumes, vol. 40, no. 12, pp. 462–467, 2007, 7th IFAC Symposium on Nonlinear Control Systems

    2007

  2. [2]

    Control barrier function based quadratic programs for safety critical systems,

    A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2017

    2017

  3. [3]

    Barrier function based model predictive control,

    A. G. Wills and W. P. Heath, “Barrier function based model predictive control,” Automatica, vol. 40, no. 8, pp. 1415–1422, 2004

    2004

  4. [4]

    The interior-point revolution in optimization: History, recent developments, and lasting consequences,

    M. H. Wright, “The interior-point revolution in optimization: History, recent developments, and lasting consequences,” Bulletin (new series) of the American Mathematical Society , vol. 42, no. 1, pp. 39–56, 2005. 14 20 15 10 5 0 5 10 15 20 x 5.0 2.5 0.0 2.5 5.0 y (a) Trajectories of the kinematic bicycle model for static constraints. A marker is depicted ...

    work page 2005

  5. [5]

    Runtime assurance for safety-critical systems: An introduction to safety filtering approaches for complex control systems,

    K. L. Hobbs, M. L. Mote, M. C. L. Abate, S. D. Coogan, and E. M. Feron, “Runtime assurance for safety-critical systems: An introduction to safety filtering approaches for complex control systems,” IEEE Control Systems Magazine, vol. 43, no. 2, pp. 28–65, 2023. 20 15 10 5 0 5 10 15 20 x 5.0 2.5 0.0 2.5 5.0 y (a) Trajectories of the kinematic unicycle model...

    work page 2023

  6. [6]

    Data-driven safety filters: Hamilton- jacobi reachability, control barrier functions, and predictive methods for uncertain systems,

    K. P. Wabersich, A. J. Taylor, J. J. Choi, K. Sreenath, C. J. Tomlin, A. D. Ames, and M. N. Zeilinger, “Data-driven safety filters: Hamilton- jacobi reachability, control barrier functions, and predictive methods for uncertain systems,” IEEE Control Systems Magazine , vol. 43, no. 5, pp. 137–177, 2023

    2023

  7. [7]

    Control barrier function based quadratic programs with application to adaptive cruise control,

    A. D. Ames, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs with application to adaptive cruise control,” in 53rd IEEE Conference on Decision and Control , 2014, pp. 6271–6278

    2014

  8. [8]

    Safety-critical control for non-affine non- linear systems with application on autonomous vehicle,

    T. D. Son and Q. Nguyen, “Safety-critical control for non-affine non- linear systems with application on autonomous vehicle,” in 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, pp. 7623–7628

    work page 2019

Show all 66 references
  1. [9]

    Decentralized merging control in traffic networks: a control barrier function approach,

    W. Xiao, C. Belta, and C. G. Cassandras, “Decentralized merging control in traffic networks: a control barrier function approach,” in Proceedings of the 10th ACM/IEEE International Conference on Cyber-Physical Systems, ser. ICCPS ’19. New York, NY , USA: Association for Comput...

    2019

  2. [10]

    Rule-based safety-critical control design using control barrier functions with application to au- tonomous lane change,

    S. He, J. Zeng, B. Zhang, and K. Sreenath, “Rule-based safety-critical control design using control barrier functions with application to au- tonomous lane change,” in 2021 American Control Conference (ACC) , 2021, pp. 178–185

    2021

  3. [11]

    Decentralized ve- hicle coordination and lane switching without switching of controllers,

    A. Frauenfelder, A. Wiltz, and D. V . Dimarogonas, “Decentralized ve- hicle coordination and lane switching without switching of controllers,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 3334–3339, 2023

    2023

  4. [12]

    Maneuvering with safety guarantees using control barrier functions,

    M. Marley, R. Skjetne, E. Basso, and A. R. Teel, “Maneuvering with safety guarantees using control barrier functions,” vol. 54, no. 16, 2021, pp. 370–377, 13th IFAC Conference on Control Applications in Marine Systems, Robotics, and Vehicles CAMS 2021

    2021

  5. [13]

    Safety-certified constrained control of maritime autonomous surface ships for automatic berthing,

    Z. Peng, C. Wang, Y . Yin, and J. Wang, “Safety-certified constrained control of maritime autonomous surface ships for automatic berthing,” IEEE Transactions on Vehicular Technology , vol. 72, no. 7, pp. 8541– 8552, 2023

    2023

  6. [14]

    Safety-critical guid- ance of underactuated marine vehicles in dynamic environments using velocity obstacles,

    A. Haraldsen, M. S. Wiig, and K. Y . Pettersen, “Safety-critical guid- ance of underactuated marine vehicles in dynamic environments using velocity obstacles,” in 2024 IEEE Conference on Control Technology and Applications (CCTA) , 2024, pp. 343–350

    2024

  7. [15]

    Combining control barrier functions and behavior trees for multi-agent underwater coverage missions,

    O. Özkahraman and P. Ögren, “Combining control barrier functions and behavior trees for multi-agent underwater coverage missions,” in 2020 59th IEEE Conference on Decision and Control (CDC), 2020, pp. 5275– 5282

    2020

  8. [16]

    Safety verification of 15 reactive controllers for uav flight in cluttered environments using barrier certificates,

    A. J. Barry, A. Majumdar, and R. Tedrake, “Safety verification of 15 reactive controllers for uav flight in cluttered environments using barrier certificates,” in 2012 IEEE International Conference on Robotics and Automation, 2012, pp. 484–490

    2012

  9. [17]

    Guaranteed safe spacecraft docking with control barrier functions,

    J. Breeden and D. Panagou, “Guaranteed safe spacecraft docking with control barrier functions,” IEEE Control Systems Letters , vol. 6, pp. 2000–2005, 2022

    2000

  10. [18]

    Collision avoidance and geofencing for fixed-wing aircraft with control barrier functions,

    T. G. Molnar, S. K. Kannan, J. Cunningham, K. Dunlap, K. L. Hobbs, and A. D. Ames, “Collision avoidance and geofencing for fixed-wing aircraft with control barrier functions,” IEEE Transactions on Control Systems Technology, pp. 1–16, 2025

    2025

  11. [19]

    Linear velocity-free visual servoing control for unmanned helicopter landing on a ship with visibility constraint,

    Y . Huang, M. Zhu, Z. Zheng, and K. H. Low, “Linear velocity-free visual servoing control for unmanned helicopter landing on a ship with visibility constraint,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 5, pp. 2979–2993, 2022

    2022

  12. [20]

    Control barrier functions for mechanical systems: Theory and application to robotic grasping,

    W. Shaw Cortez, D. Oetomo, C. Manzie, and P. Choong, “Control barrier functions for mechanical systems: Theory and application to robotic grasping,” IEEE Transactions on Control Systems Technology , vol. 29, no. 2, pp. 530–545, 2021

    2021

  13. [21]

    Safe control for soft-rigid robots with self-contact using control barrier functions,

    Z. J. Patterson, W. Xiao, E. Sologuren, and D. Rus, “Safe control for soft-rigid robots with self-contact using control barrier functions,” in 2024 IEEE 7th International Conference on Soft Robotics (RoboSoft) , 2024, pp. 151–156

    2024

  14. [22]

    Constrained robot control using control barrier functions,

    M. Rauscher, M. Kimmel, and S. Hirche, “Constrained robot control using control barrier functions,” in 2016 IEEE/RSJ International Con- ference on Intelligent Robots and Systems (IROS) , 2016, pp. 279–285

    2016

  15. [23]

    A control barrier function approach for maximizing perfor- mance while fulfilling to iso/ts 15066 regulations,

    F. Ferraguti, M. Bertuletti, C. T. Landi, M. Bonfè, C. Fantuzzi, and C. Secchi, “A control barrier function approach for maximizing perfor- mance while fulfilling to iso/ts 15066 regulations,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 5921–5928, 2020

    2020

  16. [24]

    Distributed barrier function-enabled human-in-the-loop control for multi-robot sys- tems,

    V . N. Fernandez-Ayala, X. Tan, and D. V . Dimarogonas, “Distributed barrier function-enabled human-in-the-loop control for multi-robot sys- tems,” in 2023 IEEE International Conference on Robotics and Automa- tion (ICRA), 2023, pp. 7706–7712

    2023

  17. [25]

    Control barrier functions for signal temporal logic tasks,

    L. Lindemann and D. V . Dimarogonas, “Control barrier functions for signal temporal logic tasks,” IEEE Control Systems Letters, vol. 3, no. 1, pp. 96–101, 2019

    2019

  18. [26]

    High order control lyapunov-barrier functions for temporal logic specifications,

    W. Xiao, C. A. Belta, and C. G. Cassandras, “High order control lyapunov-barrier functions for temporal logic specifications,” in 2021 American Control Conference (ACC) , 2021, pp. 4886–4891

    2021

  19. [27]

    Handling disjunctions in signal temporal logic based control through nonsmooth barrier functions,

    A. Wiltz and D. V . Dimarogonas, “Handling disjunctions in signal temporal logic based control through nonsmooth barrier functions,” in 2022 IEEE 61st Conference on Decision and Control (CDC) , 2022, pp. 3237–3242

    2022

  20. [28]

    Continuous-time control synthe- sis under nested signal temporal logic specifications,

    P. Yu, X. Tan, and D. V . Dimarogonas, “Continuous-time control synthe- sis under nested signal temporal logic specifications,” IEEE Transactions on Robotics, vol. 40, pp. 2272–2286, 2024

    2024

  21. [29]

    Exponential control barrier functions for enforcing high relative-degree safety-critical constraints,

    Q. Nguyen and K. Sreenath, “Exponential control barrier functions for enforcing high relative-degree safety-critical constraints,” in American Control Conference (ACC), 2016, pp. 322–328

    2016

  22. [30]

    High-order barrier functions: Robustness, safety and performance-critical control,

    X. Tan, W. Shaw Cortez, and D. V . Dimarogonas, “High-order barrier functions: Robustness, safety and performance-critical control,” IEEE Transactions on Automatic Control , vol. 67, no. 6, pp. 3021–3028, jun 2022

    2022

  23. [31]

    High order control barrier functions,

    W. Xiao and C. Belta, “High order control barrier functions,” IEEE Transactions on Automatic Control , 2021

    2021

  24. [32]

    Low-complexity control for a class of uncertain mimo nonlinear systems under generalized time-varying output constraints,

    F. Mehdifar, L. Lindemann, C. P. Bechlioulis, and D. V . Dimarogonas, “Low-complexity control for a class of uncertain mimo nonlinear systems under generalized time-varying output constraints,” 2024

    2024

  25. [33]

    On the equivalence between prescribed performance con- trol and control barrier functions,

    R. Namerikawa, A. Wiltz, F. Mehdifar, T. Namerikawa, and D. V . Dimarogonas, “On the equivalence between prescribed performance con- trol and control barrier functions,” in 2024 American Control Conference (ACC), 2024, pp. 2458–2463

    2024

  26. [34]

    Safe-by-design control for euler–lagrange systems,

    W. Shaw Cortez and D. V . Dimarogonas, “Safe-by-design control for euler–lagrange systems,” Automatica, vol. 146, p. 110620, 2022

    2022

  27. [35]

    A collision cone approach for control barrier functions,

    M. Tayal, B. G. Goswami, K. Rajgopal, R. Singh, T. Rao, J. Keshavan, P. Jagtap, and S. Kolathaya, “A collision cone approach for control barrier functions,” 2024

    2024

  28. [36]

    Synergistic control barrier functions with application to obstacle avoidance for nonholonomic vehicles,

    A. R. T. Mathias Marley, Roger Skjetne, “Synergistic control barrier functions with application to obstacle avoidance for nonholonomic vehicles,” American Control Conference (ACC). New Orleans, USA: American Control Conference (ACC), May 26-28 2021

    2021

  29. [37]

    Correctness guarantees for the composition of lane keeping and adaptive cruise control,

    X. Xu, J. W. Grizzle, P. Tabuada, and A. D. Ames, “Correctness guarantees for the composition of lane keeping and adaptive cruise control,” IEEE Transactions on Automation Science and Engineering , vol. 15, no. 3, pp. 1216–1229, 2018

    2018

  30. [38]

    Verification and synthesis of control barrier functions,

    A. Clark, “Verification and synthesis of control barrier functions,” in 2021 60th IEEE Conference on Decision and Control (CDC) , 2021, pp. 6105–6112

    2021

  31. [39]

    Safety verification and controller synthesis for systems with input constraints,

    H. Wang, K. Margellos, and A. Papachristodoulou, “Safety verification and controller synthesis for systems with input constraints,” arXiv, pp. 1698–1703, 2022. [Online]. Available: https://arxiv.org/abs/2204.09386

    2022 arXiv

  32. [40]

    Iterative model predictive control for piecewise systems,

    U. Rosolia and A. D. Ames, “Iterative model predictive control for piecewise systems,” IEEE Control Systems Letters , vol. 6, pp. 842–847, 2022

    2022

  33. [41]

    Receding horizon control with online barrier function design under signal temporal logic specifica- tions,

    M. Charitidou and D. V . Dimarogonas, “Receding horizon control with online barrier function design under signal temporal logic specifica- tions,” IEEE Transactions on Automatic Control , pp. 1–12, 2022

    2022

  34. [42]

    Predictive control barrier func- tions: Enhanced safety mechanisms for learning-based control,

    K. P. Wabersich and M. N. Zeilinger, “Predictive control barrier func- tions: Enhanced safety mechanisms for learning-based control,” IEEE Transactions on Automatic Control, vol. 68, no. 5, pp. 2638–2651, May 2023

    2023

  35. [43]

    An online approach to active set invariance,

    T. Gurriet, M. Mote, A. D. Ames, and E. Feron, “An online approach to active set invariance,” in 2018 IEEE Conference on Decision and Control (CDC), 2018, pp. 3592–3599

    2018

  36. [44]

    Constructive barrier cer- tificates with applications to fixed-wing aircraft collision avoidance,

    E. Squires, P. Pierpaoli, and M. Egerstedt, “Constructive barrier cer- tificates with applications to fixed-wing aircraft collision avoidance,” in 2018 IEEE Conference on Control Technology and Applications (CCTA), 2018, pp. 1656–1661

    2018

  37. [45]

    High relative degree control barrier functions under input constraints,

    J. Breeden and D. Panagou, “High relative degree control barrier functions under input constraints,” in 2021 60th IEEE Conference on Decision and Control (CDC) , 2021, pp. 6119–6124

    2021

  38. [46]

    Backup control barrier functions: Formulation and comparative study,

    Y . Chen, M. Jankovic, M. Santillo, and A. D. Ames, “Backup control barrier functions: Formulation and comparative study,” in 2021 60th IEEE Conference on Decision and Control (CDC) , 2021, pp. 6835– 6841

    2021

  39. [47]

    Predictive control barrier functions for online safety critical control,

    J. Breeden and D. Panagou, “Predictive control barrier functions for online safety critical control,” in2022 IEEE 61st Conference on Decision and Control (CDC) , 2022, pp. 924–931

    2022

  40. [48]

    Robust control barrier–value functions for safety-critical control,

    J. J. Choi, D. Lee, K. Sreenath, C. J. Tomlin, and S. L. Herbert, “Robust control barrier–value functions for safety-critical control,” in 2021 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 6814–6821

    2021

  41. [49]

    Neural lyapunov control,

    Y .-C. Chang, N. Roohi, and S. Gao, “Neural lyapunov control,” in Advances in Neural Information Processing Systems , H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett, Eds., vol. 32. Curran Associates, Inc., 2019

    2019

  42. [50]

    Learning robust output control barrier functions from safe expert demonstrations,

    L. Lindemann, A. Robey, L. Jiang, S. Das, S. Tu, and N. Matni, “Learning robust output control barrier functions from safe expert demonstrations,” IEEE Open Journal of Control Systems , vol. 3, pp. 158–172, 2024

    2024

  43. [51]

    Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control,

    C. Dawson, S. Gao, and C. Fan, “Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control,” IEEE Transactions on Robotics , vol. 39, no. 3, pp. 1749– 1767, 2023

    2023

  44. [52]

    Leveraging equivariances and sym- metries in the control barrier function synthesis,

    A. Wiltz and D. V . Dimarogonas, “Leveraging equivariances and sym- metries in the control barrier function synthesis,” 2025, in preparation

    2025

  45. [53]

    Equivariant dynamical systems,

    M. Field, “Equivariant dynamical systems,” Bulletin of the American Mathematical Society, vol. 76, no. 6, pp. 1314–1318, 1970

    1970

  46. [54]

    Equivariant systems theory and observer design,

    R. Mahony, T. Hamel, and J. Trumpf, “Equivariant systems theory and observer design,” 2020

    2020

  47. [55]

    From time-invariant to uniformly time-varying control barrier functions: A constructive approach,

    A. Wiltz and D. V . Dimarogonas, “From time-invariant to uniformly time-varying control barrier functions: A constructive approach,” in2024 IEEE 63rd Conference on Decision and Control (CDC) , 2024

    2024

  48. [56]

    Construction of control barrier functions using predictions with finite horizon,

    A. Wiltz, X. Tan, and D. V . Dimarogonas, “Construction of control barrier functions using predictions with finite horizon,” in 2023 IEEE 62nd Conference on Decision and Control (CDC) , 2023

    2023

  49. [57]

    Asymptotic stability and feedback stabilization,

    R. W. Brockett, “Asymptotic stability and feedback stabilization,” Dif- ferential geometric control theory , vol. 27, no. 1, pp. 181–191, 1983

    1983

  50. [58]

    Lyapunov functions and discontinuous stabilizing feedback,

    F. Clarke, “Lyapunov functions and discontinuous stabilizing feedback,” Annual Reviews in Control , vol. 35, no. 1, pp. 13–33, 2011

    2011

  51. [59]

    A lyapunov-like characterization of asymptotic control- lability,

    E. D. Sontag, “A lyapunov-like characterization of asymptotic control- lability,” SIAM Journal on Control and Optimization , vol. 21, no. 3, pp. 462–471, 1983

    1983

  52. [60]

    H. K. Khalil, Nonlinear systems, 3rd ed. Prentice Hall, 2002

    2002

  53. [61]

    Nonlinear controllability and observability,

    R. Hermann and A. Krener, “Nonlinear controllability and observability,” IEEE Transactions on Automatic Control , vol. 22, no. 5, pp. 728–740, 1977

    1977

  54. [62]

    Nonlinear controllability via lie theory,

    G. Haynes and H. Hermes, “Nonlinear controllability via lie theory,” SIAM Journal on Control , vol. 8, no. 4, pp. 450–460, 1970

    1970

  55. [63]

    Trajectory planning for a four-wheel-steering vehicle,

    D. Wang and F. Qi, “Trajectory planning for a four-wheel-steering vehicle,” in Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation , vol. 4, 2001, pp. 3320–3325. 16

    2001

  56. [64]

    Examples when nonlinear model predictive control is nonrobust,

    G. Grimm, M. J. Messina, S. E. Tuna, and A. R. Teel, “Examples when nonlinear model predictive control is nonrobust,” Automatica, vol. 40, no. 10, pp. 1729–1738, 2004

    2004

  57. [65]

    CasADi – A software framework for nonlinear optimization and opti- mal control,

    J. A. E. Andersson, J. Gillis, G. Horn, J. B. Rawlings, and M. Diehl, “CasADi – A software framework for nonlinear optimization and opti- mal control,” Mathematical Programming Computation , vol. 11, no. 1, pp. 1–36, 2019

    2019

  58. [66]

    min tPr0,T2s hpφpt;x0,u˚ x0,T2qq´ γt (47a) ě min tPr0,T2s hpφpt;x0,u˚ e,x0,T1qq´ γt (47b) “ min

    R. Schneider, Convex bodies : the Brunn-Minkowski theory, 2nd ed., ser. Encyclopedia of mathematics and its applications, 2014. APPENDIX Proof of Proposition 3. Let us construct in the following for each x0 P BF an input trajectory ux0 P U and its corre- sponding state traject...

    2014

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.