Momentum-Based Fully Actuated System Dynamics for Distributed Optimization

This paper studies distributed nonconvex optimization for physical multi-agent systems and proposes a momentumbased fully actuated system (Mom-FAS) framework. By using High-Order Fully Actuated (HOFA) theory, heterogeneous nonlinear agent dynamics are transformed into standardized double-integrator dynamics for upper-layer optimization design. A Hessian-regularized damping mechanism and a sigmoid-scheduled primal-dual feedback law are introduced to improve transient behavior and consensus regulation. For the nominal limit system, the analysis establishes equilibrium consistency with the KKT conditions and shows that, under a verifiable local spectral condition, strict local minimum KKT equilibria are locally exponentially stable. A transfer argument further shows that the scheduled closed-loop system preserves this local attractivity under vanishing scheduling mismatch and diminishing perturbations. Simulations illustrate the implementability of the proposed framework.