Reference Governed Distributed Safe Gradient Flow for Safe Optimal Output Agreement of Multi Agent Systems

Jul 16, 2026

This paper studies safe optimal output agreement for nonlinear multi-agent systems under output safety constraints. Existing safe feedback optimization often implements gradient-flow dynamics through plant inputs, which may require high-order control barrier functions, making design tuning-sensitive and potentially altering the steady-state optimal solution. A reference-governed two-layer architecture is proposed to separate output regulation from distributed optimization. The approach uses first-order control barrier constraints on reference gradients and a DSM-based Lyapunov design to certify transient safety, preserve optimal solutions, and ensure convergence. Simulations confirm safe convergence and advantages over HOCBF feedback schemes, including improved objective shaping to escape spurious equilibria.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

Introduction

Feedback optimization and optimal agreement

Safety constraints and control barrier functions

Reference-governor and dynamic safety margins

Proposed two-layer reference-governed architecture

Upper-layer reference gradient filtering

Lower-layer internal-model output regulation

arXiv :2607 .02192v1 [ ee ss . SY] 2 Jul 2026 Reference-Governed Distributed Safe Gradient Flow for Safe Optimal Output Agreement of Multi-Agent Systems ⋆ Zhanglin Shangguana , Wei Xiao b , Bo Yanga , Xinping Guana. a Department of Automation and Intelligent Sensing, Shanghai Jiao Tong University, Shanghai, China b Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, USA Abstract This paper studies safe optimal output agreement for nonlinear multi-agent systems with output safety constraints. Existing safe feedback optimization methods often implement gradient-flow dynamics directly through the plant input, which may require high-order control barrier functions (HOCBFs) . The resulting derivative-chain design is tuning-sensitive and can introduce additional equilibrium conditions that alter the steady-state optimal solution. We propose a reference-governed two-layer architecture that separates lower-layer output regulation from upper-layer distributed optimization. The upper layer filters the reference gradient flow through first-order control barrier function constraints, which are easier to tune and preserve the steady-state optimality structure of the original agreement problem. The lower layer uses an internal-model-based output regulator with a reference-dependent Lyapunov function, from which dynamic safety margins (DSMs) are constructed to certify transient output safety. We prove forward invariance, optimal-solution preservation under DSM-compatibility conditions, and convergence via a Lyapunov small-gain argument. Simulations validate safe convergence, show advantages over HOCBF-based feedback optimization, and demonstrate adaptive tangential objective shaping for escaping spurious equilibria induced by nonconvex obstacles. Key words: Distributed safe gradient flow; Feedback optimization; Control barrier function; Dynamic safety margin. 1 Introduction Feedback optimization has emerged as a control-oriented approach for real-time optimization of dynamical systems, closely related to extremum seeking but explicitly accounting for plant dynamics and closed-loop stability. Instead of solving a static optimization problem offline, feedback optimization uses measured outputs to steer the closed-loop steady state toward an optimal operating point [1–3] . For networked systems, this idea leads to distributed optimal agreement, where agents exchange local information to agree on an output value minimizing an aggregate objective [4] . Such formulations arise in multi-robot coordination, power networks, transportation systems, and other cyber-physical applications [5– 7] . However, optimality and stability alone are insufficient for safety-critical systems: even when a feedback ⋆ This paper was not presented at any IFAC meeting. Corresponding author Bo Yang. Email addresses: [ditto331@sjtu.edu.cn](ditto331@sjtu.edu.cn) (Zhanglin Shangguan), [weixy@mit.edu](weixy@mit.edu) (Wei Xiao), [bo.yang@sjtu.edu.cn](bo.yang@sjtu.edu.cn) (Bo Yang), [xpguan@sjtu.edu.cn](xpguan@sjtu.edu.cn) (Xinping Guan) . optimizer can steer the steady-state outputs to the optimal solution of the constrained steady-state problem, the physical outputs may violate safety constraints during transients. A common design route uses the plant’s input-to-steadystate map to implement gradient or primal-dual dynamics together with consensus terms, thereby steering the steady-state outputs to an optimal agreement point [8, 9] . Inequality constraints are often handled by projected dual or projected primal-dual dynamics [10], but these projections do not directly certify transient output safety. Control barrier functions (CBFs) enforce forward invariance of safe sets, while high-order CBFs (HOCBFs) extend this idea to safety constraints with high relative degree [11, 12] . CBF-filtered gradient flows have been developed for constrained optimization [13] and recently embedded into feedback

FAQs

How does the method certify transient output safety during tracking?

The lower layer constructs dynamic safety margins (DSMs) using a reference-dependent Lyapunov function within an internal-model-based output regulator. DSM-compatibility conditions enable forward invariance and guarantee transient safety while preserving the optimal solution and ensuring convergence.

Jul 16, 2026

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