Preset-Time Distributed Optimization for Nonlinear Multiagent Systems With a Time-Varying Equality Constraint Over Directed Networks

This work focuses on a constrained distributed optimization problem for nonlinear multiagent systems over directed communication networks. Under the information constraint that each agent observes only its own objective function and resource signals, a distributed observer is devised to locally reconstruct the constraint-related signals and Hessian-related information needed for optimization. Using these estimates, a preset-time (PST) distributed optimization scheme is formulated for the problem subject to a time-varying equality constraint and guarantees convergence to the optimal solution within a user-assigned time, irrespective of algorithm parameters. In contrast to existing prescribed-time optimization methods, the proposed approach applies to directed networks without requiring weight balance. Moreover, feasible initialization is not required, and the equality constraint is satisfied exactly at the PST and thereafter. The effectiveness and the practical applicability of the proposed algorithm are validated via an economic dispatch problem in power systems.