MAD-PINN: A Decentralized Physics-Informed Machine Learning Framework for Safe and Optimal Multi-Agent Control

Manan Tayal, Aditya Singh, Shishir Kolathaya, Somil Bansal

Keywords: Multi-Agent Systems, Safe Control, Physics-Informed Neural Networks, Hamilton–Jacobi Reachability

TL;DR: MAD-PINN is a decentralized physics-informed machine learning framework that achieves safe and optimal control in large multi-agent systems using local interactions and reachability-guided coordination.

Abstract: Co-optimizing safety and performance in large-scale multi-agent systems remains a fundamental challenge. Existing approaches based on multi-agent reinforcement learning (MARL), safety filtering, or Model Predictive Control (MPC) either lack strict safety guarantees, suffer from conservatism, or fail to scale effectively. We propose MAD-PINN, a decentralized physics-informed machine learning framework for solving the multi-agent state-constrained optimal control problem (MASC-OCP). Our method leverages an epigraph-based reformulation of SC-OCP to simultaneously capture performance and safety, and approximates its solution via a physics-informed neural network. Scalability is achieved by training the SC-OCP value function on reduced-agent systems and deploying them in a decentralized fashion, where each agent relies only on local observations of its neighbours for decision-making. To further enhance safety and efficiency, we introduce an Hamilton-Jacobi (HJ) reachability-based neighbour selection strategy to prioritize safety-critical interactions, and a receding-horizon policy execution scheme that adapts to dynamic interactions while reducing computational burden. Experiments on multi-agent navigation tasks demonstrate that MAD-PINN achieves superior safety–performance trade-offs, maintains scalability as the number of agents grows, and consistently outperforms state-of-the-art baselines.

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Submission Number: 2