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Feasibility-Guaranteed Safety-Critical Control with Applications to Heterogeneous Platoons

Shuo Liu, Wei Xiao, Calin A. Belta

TL;DR

This work tackles safety-critical control under tight actuation limits by integrating a general feasibility constraint with a new auxiliary-function-based CBF to guarantee that the CBF-CLF-QP optimization remains feasible while enforcing safety. The authors extend existing feasibility approaches to general affine systems using a time-varying auxiliary variable and an exponential shaping function, ensuring compatibility among hard constraints and preventing abrupt control changes. The method is validated on a heterogeneous ACC platoon, where it yields safer inter-vehicle gaps and smoother, more energy-efficient control compared to baseline CBF-CLF-QP formulations. The approach offers a principled, generalizable path to maintain safety and feasibility in constrained optimal control applications with multiple, time-varying inputs.

Abstract

This paper studies safety and feasibility guarantees for systems with tight control bounds. It has been shown that stabilizing an affine control system while optimizing a quadratic cost and satisfying state and control constraints can be mapped to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBF) and Control Lyapunov Functions (CLF). One of the main challenges in this method is that the QP could easily become infeasible under safety constraints of high relative degree, especially under tight control bounds. Recent work focused on deriving sufficient conditions for guaranteeing feasibility. The existing results are case-dependent. In this paper, we consider the general case. We define a feasibility constraint and propose a new type of CBF to enforce it. Our method guarantees the feasibility of the above mentioned QPs, while satisfying safety requirements. We demonstrate the proposed method on an Adaptive Cruise Control (ACC) problem for a heterogeneous platoon with tight control bounds, and compare our method to existing CBF-CLF approaches. The results show that our proposed approach can generate gradually transitioned control (without abrupt changes) with guaranteed feasibility and safety.

Feasibility-Guaranteed Safety-Critical Control with Applications to Heterogeneous Platoons

TL;DR

This work tackles safety-critical control under tight actuation limits by integrating a general feasibility constraint with a new auxiliary-function-based CBF to guarantee that the CBF-CLF-QP optimization remains feasible while enforcing safety. The authors extend existing feasibility approaches to general affine systems using a time-varying auxiliary variable and an exponential shaping function, ensuring compatibility among hard constraints and preventing abrupt control changes. The method is validated on a heterogeneous ACC platoon, where it yields safer inter-vehicle gaps and smoother, more energy-efficient control compared to baseline CBF-CLF-QP formulations. The approach offers a principled, generalizable path to maintain safety and feasibility in constrained optimal control applications with multiple, time-varying inputs.

Abstract

This paper studies safety and feasibility guarantees for systems with tight control bounds. It has been shown that stabilizing an affine control system while optimizing a quadratic cost and satisfying state and control constraints can be mapped to a sequence of Quadratic Programs (QPs) using Control Barrier Functions (CBF) and Control Lyapunov Functions (CLF). One of the main challenges in this method is that the QP could easily become infeasible under safety constraints of high relative degree, especially under tight control bounds. Recent work focused on deriving sufficient conditions for guaranteeing feasibility. The existing results are case-dependent. In this paper, we consider the general case. We define a feasibility constraint and propose a new type of CBF to enforce it. Our method guarantees the feasibility of the above mentioned QPs, while satisfying safety requirements. We demonstrate the proposed method on an Adaptive Cruise Control (ACC) problem for a heterogeneous platoon with tight control bounds, and compare our method to existing CBF-CLF approaches. The results show that our proposed approach can generate gradually transitioned control (without abrupt changes) with guaranteed feasibility and safety.
Paper Structure (12 sections, 3 theorems, 33 equations, 2 figures)

This paper contains 12 sections, 3 theorems, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation and Approach
  4. Feasibility Constraint
  5. Controller Design for Safety and Feasibility
  6. Case Study and Simulations
  7. Vehicle Dynamics
  8. Vehicle Limitations
  9. Implementation with Auxiliary-Function-Based CBFs
  10. Implementation with HOCBFs without Feasibility Constraint
  11. Simulation Results
  12. Conclusion and Future Work

Key Result

Theorem 1

Given a HOCBF $b(\boldsymbol{x})$ from Def. def:HOCBF with corresponding sets $\mathcal{C}_{0}, \dots,\mathcal{C}_{m-1}$ defined by eq:sequence-set1, if $\boldsymbol{x}(0) \in \mathcal{C}_{0}\cap \dots \cap \mathcal{C}_{m-1},$ then any Lipschitz controller $\boldsymbol{u}$ that satisfies the inequal

Figures (2)

  • Figure 1: Case 1-Feasibility constraint enhances feasibility for solving Prob. \ref{['prob:ACC-prob']}. The hyperparameters are set as $k_{2,1}=k_{2,2}=k_{3,1}=k_{3,2}=1,l_{2,F}=l_{3,F}=0.1.$ The lower control bounds are $c_{2,d}=0.4,c_{3,d}=0.35.$ Note that without feasibility constraint, the deceleration of the $2^{nd}$(blue), $3^{rd}$(red) vehicles exceeds deceleration bound, therefore the control bounds are violated (as shown by dashed lines in (a)), which causes infeasibility even though the safety is satisfied as shown in (c).
  • Figure 2: Case 2-Feasibility constraint enhances safety for solving Prob. \ref{['prob:ACC-prob']}. The hyperparameters are set as $k_{2,1}=k_{2,2}=k_{3,1}=k_{3,2}=1,l_{2,F}=l_{3,F}=0.05.$ The lower control bounds are $c_{2,d}=0.2,c_{3,d}=0.25$ (tighter than Fig. \ref{['fig:feasibility enhanced']}). Note that without feasibility constraint, the $b(\boldsymbol{x})$ of the $2^{nd}$(blue), $3^{rd}$(red) vehicles exceeds safety bound, therefore the safe distance between vehicles can be negative (as shown by dashed lines in (c)), which causes danger even though the control bounds are satisfied as shown in (a).

Theorems & Definitions (12)

  • Definition 1: Class $\kappa$ function Khalil:1173048
  • Definition 2
  • Definition 3
  • Definition 4: HOCBF xiao2021high
  • Theorem 1: Safety Guarantee xiao2021high
  • Definition 5: CLF ames2012control
  • Definition 6: Feasibility Constraint
  • Lemma 1
  • proof
  • Remark 1
  • ...and 2 more