Control Barrier Function for Unknown Systems: An Approximation-free Approach

2025-11-28

AI Summary

This paper addresses the prescribed-time reach-avoid (PT-RA) control problem for nonlinear systems with unknown dynamics operating in environments with moving obstacles. Method: We propose a Control Barrier Function–Quadratic Programming (CBF-QP) framework that requires neither online learning nor estimation of uncertainty bounds. A virtual system generates a reference trajectory satisfying both safety and goal constraints, while a novel approximation-free feedback law—based on a Virtual Constraint Zone (VCZ)—strictly confines the system state within a time-varying safe set. Contribution/Results: By innovatively integrating time-varying compact obstacle and goal sets, our approach guarantees simultaneous prescribed-time convergence to the target and end-to-end safety—even under unknown dynamics. Extensive simulations demonstrate real-time safety and guaranteed goal attainment in the presence of dynamic obstacles and model uncertainties.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: Behavior Learning & Control

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Addresses prescribed-time reach-avoid control for unknown nonlinear systems
• Eliminates need for online model learning or uncertainty estimation
• Ensures safety and target reachability under dynamic constraints without model identification

Innovation

• Approximation-free CBF-QP on virtual system
• Virtual Confinement Zone ensures safety without learning
• Guarantees real-time safety under unknown dynamics