A Preassigned-Time Distributed Optimization Protocol for Resource Allocation via a Novel Convergence Theorem

This manuscript introduces a novel preassigned-time distributed optimization protocol for resource allocation in multiagent systems, addressing both local convex set constraints and global equality constraints. The protocol operates through two sequential phases: initially, each agent’s state is deterministically driven into its feasible set within a prespecified time; subsequently, global equality constraints are continuously maintained while progressively converging to the optimal solution, achieving exact optimization within the total preassigned time. Distinct from conventional finite-time, fixed-time, or predefined-time distributed algorithms, our framework innovatively employs a state-based generator mechanism. A key advantage is the settling time’s invariance to both initial conditions and system parameters, enabling precise offline determination of convergence timelines and offering substantial practical benefits for real-time implementations. Numerical experiments validate the theoretical soundness and practical efficacy of the proposed methodology in resource-constrained distributed coordination scenarios.