Optimization-Free Constrained Control with Guaranteed Recursive Feasibility: A CBF-Based Reference Governor Approach

2026-04-05

AI Summary

This work addresses the challenges of traditional constrained control methods, which rely on online optimization and often fail to guarantee recursive feasibility. To overcome these limitations, the paper proposes a safety-aware control framework that integrates an Explicit Reference Governor (ERG) with Control Barrier Functions (CBFs). By modeling reference updates as virtual control inputs of an augmented system and constructing a smooth barrier function based on dynamic safety margins and soft-min aggregation, the approach achieves closed-loop safety without requiring online optimization. Recursive feasibility of safety constraints is ensured at the design level through the forward invariance of Lyapunov sublevel sets, yielding an explicit, closed-form reference update law. Theoretical analysis establishes asymptotic convergence of the closed-loop system, and simulations demonstrate that the proposed method maintains rigorous safety guarantees while achieving performance comparable to conventional ERG schemes.

Abstract

This letter presents a constrained control framework that integrates Explicit Reference Governors (ERG) with Control Barrier Functions (CBF) to ensure recursive feasibility without online optimization. We formulate the reference update as a virtual control input for an augmented system, governed by a smooth barrier function constructed from the softmin aggregation of Dynamic Safety Margins (DSMs). Unlike standard CBF formulations, the proposed method guarantees the feasibility of safety constraints by design, exploiting the forward invariance properties of the underlying Lyapunov level sets. This allows for the derivation of an explicit, closed-form reference update law that strictly enforces safety while minimizing deviation from a nominal reference trajectory. Theoretical results confirm asymptotic convergence, and numerical simulations demonstrate that the proposed method achieves performance comparable to traditional ERG frameworks.

Problem

• Constrained Control
• Recursive Feasibility
• Control Barrier Functions
• Reference Governor
• Safety Constraints

Innovation

• Control Barrier Functions
• Explicit Reference Governor
• Recursive Feasibility
• Optimization-Free Control
• Dynamic Safety Margins