Distributed Fixed/Preassigned-Time Optimization Based on Piecewise Power-Law Design

The problem of fixed-time (FXT) and preassigned-time (PAT) optimization is concerned in this article based on multiagent systems (MASs) and power-law algorithms. Under the framework of strong convexity of the cost functions, two types of piecewise algorithms are proposed, which ensure that the FXT optimization can be solved either by first achieving the FXT consensus or by first achieving local optimization. Correspondingly, the PAT optimization problem is also considered by designing several piecewise protocols, where the finished time of optimization can be arbitrary prescribed according to actual demands. Furthermore, these piecewise power-law algorithms on the weighted undirected graphs are generalized to the weighted digraphs. Finally, by providing two numerical examples, the presented algorithms are further verified.