Distributed finite-time optimization algorithms for multi-agent systems under directed graphs

Existing distributed finite-time optimization algorithms for continuous-time multi-agent systems require either undirected graphs or weight balanced digraphs, and distributed finite-time optimization problems for weight unbalanced digraphs are still great challenging. Thus, the distributed finite-time optimization problems for continuous-time multi-agent systems with strongly convex local cost functions are investigated under directed graphs in this article. First, a distributed finite-time gradient estimator is constructed by using non-smooth analysis and algebraic graph theory, then distributed finite-time optimization algorithms and piecewise distributed finite-time optimization algorithms are proposed based on the designed gradient estimator. The new proposed distributed finite-time optimization algorithms which only require strongly connected graphs relax the balanced requirement. Furthermore, the communication bandwidth of systems could be saved by deploying the proposed piecewise distributed finite-time optimization algorithms since the information exchange in the optimization process is reduced. Finally, simulation examples are given to verify the effectiveness of proposed distributed optimization algorithms.