Privacy‐Preserving Data‐Driven Distributed MPC for Heterogeneous Nonlinear Multi‐Agent Systems

ABSTRACT Distributed model predictive control (DMPC) is a cornerstone for coordinating multi‐agent systems, yet simultaneously ensuring data privacy, handling unknown nonlinear dynamics, and managing heterogeneous constraints remains an open challenge. This paper proposes a privacy‐preserving DMPC framework for heterogeneous nonlinear multi‐agent systems subject to coupled global constraints. Unlike existing methods that rely on linearized models or homogeneous assumptions, we introduce a data‐driven approach based on kernel ridge regression (KRR) to capture local nonlinear dynamics within a reproducing kernel Hilbert space (RKHS). To enable privacy‐preserving coordination without sacrificing performance, we develop an inertial differentially‐private distributed dual‐gradient (IDP‐DDG) algorithm. This algorithm integrates a momentum‐based acceleration mechanism to counteract the convergence slowdown typically caused by differential‐privacy noise, making it well suited for real‐time control. We provide theoretical guarantees, establishing that the proposed scheme ensures ‐differential privacy, almost sure convergence to the global optimum, recursive feasibility, and practical (ultimately bounded) closed‐loop stability. Numerical simulations on a formation of quadrotors validate the framework's ability to achieve consensus and constraint satisfaction despite significant privacy‐preserving noise.