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Neural Cooperative Reach-While-Avoid Certificates for Interconnected Systems

Jingyuan Zhou, Haoze Wu, Kaidi Yang

TL;DR

This work proposes neural cooperative reach-while-avoid certificates with Dynamic-Localized Vector Control Lyapunov and Barrier Functions, which capture cooperative dynamics through state-dependent neighborhood structures and provide decentralized certificates for global exponential stability and safety.

Abstract

Providing formal guarantees for neural network-based controllers in large-scale interconnected systems remains a fundamental challenge. In particular, using neural certificates to capture cooperative interactions and verifying these certificates at scale is crucial for the safe deployment of such controllers. However, existing approaches fall short on both fronts. To address these limitations, we propose neural cooperative reach-while-avoid certificates with Dynamic-Localized Vector Control Lyapunov and Barrier Functions, which capture cooperative dynamics through state-dependent neighborhood structures and provide decentralized certificates for global exponential stability and safety. Based on the certificates, we further develop a scalable training and verification framework that jointly synthesizes controllers and neural certificates via a constrained optimization objective, and leverages a sufficient condition to ensure formal guarantees considering modeling error. To improve scalability, we introduce a structural reuse mechanism to transfer controllers and certificates between substructure-isomorphic systems. The proposed methodology is validated with extensive experiments on multi-robot coordination and vehicle platoons. Results demonstrate that our framework ensures certified cooperative reach-while-avoid while maintaining strong control performance.

Neural Cooperative Reach-While-Avoid Certificates for Interconnected Systems

TL;DR

This work proposes neural cooperative reach-while-avoid certificates with Dynamic-Localized Vector Control Lyapunov and Barrier Functions, which capture cooperative dynamics through state-dependent neighborhood structures and provide decentralized certificates for global exponential stability and safety.

Abstract

Providing formal guarantees for neural network-based controllers in large-scale interconnected systems remains a fundamental challenge. In particular, using neural certificates to capture cooperative interactions and verifying these certificates at scale is crucial for the safe deployment of such controllers. However, existing approaches fall short on both fronts. To address these limitations, we propose neural cooperative reach-while-avoid certificates with Dynamic-Localized Vector Control Lyapunov and Barrier Functions, which capture cooperative dynamics through state-dependent neighborhood structures and provide decentralized certificates for global exponential stability and safety. Based on the certificates, we further develop a scalable training and verification framework that jointly synthesizes controllers and neural certificates via a constrained optimization objective, and leverages a sufficient condition to ensure formal guarantees considering modeling error. To improve scalability, we introduce a structural reuse mechanism to transfer controllers and certificates between substructure-isomorphic systems. The proposed methodology is validated with extensive experiments on multi-robot coordination and vehicle platoons. Results demonstrate that our framework ensures certified cooperative reach-while-avoid while maintaining strong control performance.
Paper Structure (27 sections, 4 theorems, 68 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 27 sections, 4 theorems, 68 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary and Problem Statement
  4. Preliminary
  5. Metzler matrix.
  6. Hurwitz matrix.
  7. Problem Statement
  8. Neural Cooperative Reach-While-Avoid Certificates
  9. Framework for Synthesizing and Verifying Cooperative RWA Certificates
  10. Control Policy Synthesis
  11. Verification Formulation
  12. Scalability Analysis
  13. Numerical Simulation
  14. System Dynamics
  15. Simulation Settings
  16. ...and 12 more sections

Key Result

Theorem 1

Suppose $V$ is a DL-VCLF satisfying the conditions in Def. def:DL-VCLFs. If for each $i\in\mathcal{N}$, there exists locally Lipschitz continuous control input $\bm{u} := (u_1, \dots, u_q) \in \mathbb{R}^{q\times m}$ such that the resulting closed-loop trajectories of the interconnected system eq: s

Figures (6)

  • Figure 1: Overview of the proposed framework for controller synthesis and neural certificate verification in interconnected systems.
  • Figure 2: Agent trajectories under cooperative vs. non-cooperative control.
  • Figure 3: Learned certificates for Agent 0.
  • Figure 4: Minimum distance to obstacles over time.
  • Figure 5: Inter-agent distance statistics.
  • ...and 1 more figures

Theorems & Definitions (16)

  • Definition 1: Multi-Agent Reach–While–Avoid Task
  • Definition 2: Global asymptotic stability
  • Remark 1
  • Definition 3: DL-VCLF
  • Theorem 1: GES with DL-VCLF
  • Definition 4: DL-VCBF
  • Theorem 2: Forward-invariant safe set with DL-VCBF
  • Definition 5: Cooperative Reach-While-Avoid Certificate
  • Remark 2
  • Theorem 3: Sufficient Conditions for Co-RWA via Discrete Time Verification
  • ...and 6 more