A Novel Protocol for Fixed-Time Distributed Optimization Over Networks Based on Zero-Gradient-Sum Strategy

Different from existing protocols for achieving fixed-time convergence, a novel fixed-time protocol with an adaptive gain is proposed for solving the distributed optimization problem over networks. Based on the zero-gradient-sum straetgy, the problem will reduced to the fixed-time consensus problem and the convergence time is determined by the frequency of a sine function. Besides, some comments on the practical implementation are also given and it is found that the proposed protocol maintains strong robustness to input saturations. Two illustrative examples are finally provided to validate all the mentioned results.