Momentum-Based Distributed Continuous-Time Nonconvex Optimization of Nonlinear Multi-Agent Systems via Timescale Separation

This study addresses the distributed nonconvex optimization problem for nonlinear multi-agent systems over a weight-balanced and quasi-strongly connected graph. The purpose is to steer all agents to the optimum of a given global objective function with inputs and outputs on the basis of the actual partial information related to the input and output. Novel momentum-based distributed optimal coordinators are designed to achieve this objective, and the local objective functions should be analytic to replace its convexity. An interconnected system with different timescales is established by converting the overall closed-loop system involving the module of momentum-based distributed optimal coordinators and nonlinear multi-agent systems. The singular perturbation approach is applied to deal with the overall interconnected closed-loop system by timescale separation. A numerical example and an application example with four firefighting unmanned aerial vehicles (UAVs) verify the superiority and effectiveness of the proposed distributed method and extended algorithms. Three momentum-based gradient descent algorithms (basic momentum-based, momentum-based Newton, and projected momentum-based gradient flows) are compared and analyzed.