Distributed Prescribed-Time Optimization with Time-Varying Cost: Zero-Gradient-Sum Scheme

This paper proposes a zero-gradient-sum-based time-varying distributed prescribed-time optimization algorithm for single integrator dynamics. The algorithm introduces a prescribed-time sliding mode term aimed at attaining zero-gradient-sum, alongside a sliding-mode controller designed to ensure consensus among agents' states within a prescribed-time limit. Notably, the algorithm eliminates the need for initial condition constraints and local minimization. The criteria for achieving consensus and optimizing multi-agent systems are derived from optimization theory and Lyapunov stability theory. Finally, the superior convergence efficiency of the algorithm is verified through a power-sharing case study.