Predictive Control Barrier Functions for Discrete-Time Linear Systems with Unmodeled Delays

2025-10-01

AI Summary

For discrete-time linear systems with unmodeled input delays, existing discrete-time control barrier function (CBF) methods require auxiliary barrier functions when the relative degree exceeds one, leading to implementation complexity and conservative safety sets. This paper proposes a predictive control barrier function (PCBF) framework: by extending the prediction horizon, it constructs an equivalent virtual system with relative degree one, enabling direct barrier function definition in the original state space—thereby eliminating the need for auxiliary functions. Consequently, the safety set precisely coincides with the PCBF superlevel set, significantly reducing conservatism and simplifying implementation. Theoretical analysis guarantees recursive feasibility and safety. Experiments on a double-integrator system with input delay and a constrained-position quadrotor demonstrate high-precision, robust safe control performance.

Technology Category

• Humans and AI: Human-Aware Planning and Behavior Prediction
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper introduces a predictive control barrier function (PCBF) framework for enforcing state constraints in discrete-time systems with unknown relative degree, which can be caused by input delays or unmodeled input dynamics. Existing discrete-time CBF formulations typically require the construction of auxiliary barrier functions when the relative degree is greater than one, which complicates implementation and may yield conservative safe sets. The proposed PCBF framework addresses this challenge by extending the prediction horizon to construct a CBF for an associated system with relative degree one. As a result, the superlevel set of the PCBF coincides with the safe set, simplifying constraint enforcement and eliminating the need for auxiliary functions. The effectiveness of the proposed method is demonstrated on a discrete-time double integrator with input delay and a bicopter system with position constraints.

Problem

• Enforcing state constraints in discrete-time systems with unknown delays
• Addressing high relative degree issues in control barrier functions
• Simplifying safe set construction without auxiliary barrier functions

Innovation

• Predictive control barrier functions handle unmodeled delays
• Extended prediction horizon creates relative degree one system
• Eliminates need for auxiliary barrier function construction