Distributed Predefined-Time Optimal Control Algorithm for Nonconvex Optimization of MASs

This paper delves into a class of distributed nonconvex optimization control (DNOC) problems for multiagent systems (MASs), aiming to attain consensus among agents while minimizing the collective sum of local cost functions, referred to as the global cost function, through local information exchange. To accomplish this objective, it is introduced a novel distributed predefined-time optimal (DPTO) control algorithm. We prove that the proposed DPTO control algorithm guides the system states towards convergence to the global optimal solution within a user-defined time frame, provided that the global cost function satisfies the Polyak-Lojasiewicz condition, which is less stringent than the standard strong convexity condition. Finally, theoretical findings are substantiated through simulation studies.