Approximation-Free Control Barrier Functions for Prescribed-Time Reach-Avoid of Unknown Systems

TL;DR

This paper introduces an approximation-free control method for nonlinear systems that guarantees safety and target reachability within a prescribed time, without requiring online learning or model estimation.

Contribution

The proposed framework achieves prescribed-time reach-avoid control for unknown nonlinear systems without online model learning or uncertainty bounds, using a CBF-based virtual system and confinement law.

Findings

Ensures real-time safety and prescribed-time target reachability.

Effective obstacle avoidance demonstrated in simulations.

No explicit model identification or offline precomputation needed.

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.