Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Proxy Control Barrier Functions: Integrating Barrier-Based and Lyapunov-Based Safety-Critical Control Design

Yujie Wang, Xiangru Xu

TL;DR

The paper addresses safety for strict-feedback systems with potentially unknown dynamics, where traditional CBF methods struggle with unknown control directions and disturbances. It introduces Proxy Control Barrier Functions (PCBF) that modularize the problem into a proxy subsystem (CBF-based safety) and a virtual tracking subsystem (Lyapunov-based stabilization), enabling safety via a CBF-QP while keeping the tracking error within a bound $|e(t)|\le\rho(t)$. Key contributions include a constructive Theorem 1 guaranteeing a nonempty feasible set for the CBF controller and safety, a model-free/tracking corollary for the Lyapunov-based subsystem, and a DOB-PCBF extension (Theorem 2) using a filter-based disturbance observer with backstepping to handle mismatched disturbances, all validated by simulations. This framework broadens the applicability of CBF-based safety to systems with unknown dynamics, reduces CBF design complexity by leveraging a proxy model, and yields a robust, modular safe-control approach for high-order systems with disturbances.

Abstract

This work introduces a novel Proxy Control Barrier Function (PCBF) scheme that integrates barrier-based and Lyapunov-based safety-critical control strategies for strict-feedback systems with potentially unknown dynamics. The proposed method employs a modular design procedure, decomposing the original system into a proxy subsystem and a virtual tracking subsystem that are controlled by the control barrier function (CBF)-based and Lyapunov-based controllers, respectively. By integrating these separately designed controllers, the overall system's safety is ensured. Moreover, a new filter-based disturbance observer is utilized to design a PCBF-based safe controller for strict-feedback systems subject to mismatched disturbances. This approach broadens the class of systems to which CBF-based methods can be applied and significantly simplifies CBF construction by requiring only the model of the proxy subsystem. The effectiveness of the proposed method is demonstrated through numerical simulations.

Proxy Control Barrier Functions: Integrating Barrier-Based and Lyapunov-Based Safety-Critical Control Design

TL;DR

The paper addresses safety for strict-feedback systems with potentially unknown dynamics, where traditional CBF methods struggle with unknown control directions and disturbances. It introduces Proxy Control Barrier Functions (PCBF) that modularize the problem into a proxy subsystem (CBF-based safety) and a virtual tracking subsystem (Lyapunov-based stabilization), enabling safety via a CBF-QP while keeping the tracking error within a bound . Key contributions include a constructive Theorem 1 guaranteeing a nonempty feasible set for the CBF controller and safety, a model-free/tracking corollary for the Lyapunov-based subsystem, and a DOB-PCBF extension (Theorem 2) using a filter-based disturbance observer with backstepping to handle mismatched disturbances, all validated by simulations. This framework broadens the applicability of CBF-based safety to systems with unknown dynamics, reduces CBF design complexity by leveraging a proxy model, and yields a robust, modular safe-control approach for high-order systems with disturbances.

Abstract

This work introduces a novel Proxy Control Barrier Function (PCBF) scheme that integrates barrier-based and Lyapunov-based safety-critical control strategies for strict-feedback systems with potentially unknown dynamics. The proposed method employs a modular design procedure, decomposing the original system into a proxy subsystem and a virtual tracking subsystem that are controlled by the control barrier function (CBF)-based and Lyapunov-based controllers, respectively. By integrating these separately designed controllers, the overall system's safety is ensured. Moreover, a new filter-based disturbance observer is utilized to design a PCBF-based safe controller for strict-feedback systems subject to mismatched disturbances. This approach broadens the class of systems to which CBF-based methods can be applied and significantly simplifies CBF construction by requiring only the model of the proxy subsystem. The effectiveness of the proposed method is demonstrated through numerical simulations.
Paper Structure (15 sections, 19 equations, 3 figures)

This paper contains 15 sections, 19 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Motivation and Problem Formulation
  3. Motivation
  4. Problem Formulation
  5. PCBF-based Control Design
  6. System Decomposition
  7. Proxy Subsystem Control Design
  8. Virtual Tracking Subsystem Control Design
  9. Safety Guarantee of the Overall System
  10. DOB-PCBF Control Design
  11. Conclusion
  12. Proof of Theorem \ref{['theorem:proxy']}
  13. Proof of Corollary \ref{['corollary:tracking']}
  14. Proof of Lemma \ref{['corollary:filter']}
  15. Proof of Theorem \ref{['theorem:systemmismatchblf']}

Figures (3)

  • Figure 1: Illustration of the proposed PCBF control scheme. The original system is decomposed into two subsystems that are controlled by CBF-based and Lyapunov-based methods, respectively. The PCBF method is modular and inherits advantages of both CBF-based and Lyapunov-based approaches.
  • Figure 2: Simulation results of Example \ref{['example:ship']}. The safety is always respected as the trajectory of $\psi$ stays inside the safe region whose boundary is represented by the dashed red line.
  • Figure 3: Simulation results of Example \ref{['example:mismatch']}. All three methods can ensure safety but the DOB-PCBF method has the best tracking performance and the smoothest control profile.