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Adaptive Safety-Critical Control for a Class of Nonlinear Systems with Parametric Uncertainties: A Control Barrier Function Approach

Yujie Wang, Xiangru Xu

TL;DR

This work addresses safety in nonlinear control with parametric uncertainties in both drift terms and input matrices by developing a singularity-free adaptive control barrier function (aCBF) framework. The safe controller is obtained by solving a nonlinear program with a closed-form solution, and safety guarantees rely on nominal parameter bounds rather than online estimates to avoid infeasibility. A data-driven tightening procedure further reduces conservatism by refining bounds on unknowns using collected data. Numerical simulations demonstrate safe operation and performance gains from the data-driven augmentation, highlighting practical potential for safety-critical learning-enabled control.

Abstract

This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control-input matrices. The method combines control barrier functions and adaptive laws to generate a safe controller through a nonlinear program with an explicitly given closed-form solution. The proposed approach verifies the non-emptiness of the admissible control set independently of online parameter estimations, which can ensure the safe controller is singularity-free. A data-driven algorithm is also developed to improve the performance of the proposed controller by tightening the bounds of the unknown parameters. The effectiveness of the control scheme is demonstrated through numerical simulations.

Adaptive Safety-Critical Control for a Class of Nonlinear Systems with Parametric Uncertainties: A Control Barrier Function Approach

TL;DR

This work addresses safety in nonlinear control with parametric uncertainties in both drift terms and input matrices by developing a singularity-free adaptive control barrier function (aCBF) framework. The safe controller is obtained by solving a nonlinear program with a closed-form solution, and safety guarantees rely on nominal parameter bounds rather than online estimates to avoid infeasibility. A data-driven tightening procedure further reduces conservatism by refining bounds on unknowns using collected data. Numerical simulations demonstrate safe operation and performance gains from the data-driven augmentation, highlighting practical potential for safety-critical learning-enabled control.

Abstract

This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control-input matrices. The method combines control barrier functions and adaptive laws to generate a safe controller through a nonlinear program with an explicitly given closed-form solution. The proposed approach verifies the non-emptiness of the admissible control set independently of online parameter estimations, which can ensure the safe controller is singularity-free. A data-driven algorithm is also developed to improve the performance of the proposed controller by tightening the bounds of the unknown parameters. The effectiveness of the control scheme is demonstrated through numerical simulations.
Paper Structure (12 sections, 38 equations, 5 figures)

This paper contains 12 sections, 38 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries & Problem Statement
  3. Notation
  4. Control Barrier Function
  5. Problem Formulation
  6. aCBF-NLP-based Safe Control Design
  7. aCBF-NLP-Based Control Design
  8. Closed-form Solution to the aCBF-NLP
  9. Extension to More General Systems
  10. Tightening Parameter Bounds via a Data-driven Approach
  11. Simulation
  12. Conclusion

Figures (5)

  • Figure 1: Main results of this paper.
  • Figure 2: Evolution of the state variable $x$ of Example \ref{['example1']}. It can be seen that both the aCBF-NLP controller and the data-driven augmented aCBF-NLP controller can ensure safety as the trajectories of $x$ always stay in the safe region (i.e., above the dashed red line). One can also see that, when the data-driven technique developed in Theorem \ref{['theoremdatadriven']} is adopted, the aCBF-NLP controller has a better control performance.
  • Figure 3: Simulation results of Example \ref{['example2']}. The aCBF-NLP controller, either with or without the data-driven technique, can ensure safety of the system. When combined with the data-driven techniques, the aCBF-NLP controller has a slightly better control performance in terms of maintaining the desired velocity.
  • Figure 4: Simulation results of Example \ref{['example3']} using the control scheme shown in \ref{['cbfnlp1']}. From (c) it can be seen that the proposed aCBF-NLP-based controller can guarantee safety as $h$ is always non-negative; from (a) it can be seen that, if the data-driven techniques are adopted, the control performance becomes less conservative since $x_1$ can track the reference trajectory better inside the safe region.
  • Figure 5: Simulation results of Example \ref{['example3']} using the control strategy shown in \ref{['cbfnlpgeneral']}. From (c) it can be seen that the aCBF-NLP-based controller obtained by solving \ref{['cbfnlpgeneral']} can guarantee safety; however, the control performance is unsatisfactory (i.e., the tracking performance of the desired controller is not well-preserved) due to the intrinsic conservatism discussed in Remark \ref{['remark:generaldisadvantage']}.

Theorems & Definitions (6)

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