Finite-Time Distributed Optimization with Quadratic Objective Functions under Uncertain Information

This paper presents distributed algorithms for finite-time convex optimization problem of multi-agent systems. The uncertain information comes from the noise corruption or interference in the communication as well as computation performed by the agents. The objective is to design distributed algorithms so that a team of agents, each with its own private cost function and communicating over an undirected graph, seeks to minimize the sum of local objective functions in a finite time. Specifically, a distributed algorithm with robust consensus strategies is proposed to solve this distributed optimization problem so that the optimal solution can be estimated in a finite time. The developed algorithm is applied to the economic dispatch problem and it shows that under the proposed algorithms, the optimal solution can be achieved in a finite time, while satisfying both the global generation-demand constraints and local generation capacity constraints.