Distributed Fixed-Time Optimization With Time-Varying Cost: Zero-Gradient-Sum Scheme

This note proposes a zero-gradient-sum method for first-order integrator dynamics that can solve time-varying distributed convex optimization problem in fixed-time. The algorithm is composed of a fixed-time sliding mode term for achieving zero-gradient-sum, and a fixed-time controller involving the sign function for attaining state consensus among agents. It requires only local state interaction among neighboring agents, and hence, has lower communication cost. The effectiveness of the algorithm is demonstrated by a power sharing case study.