Distributed Finite-Time Optimization for Disturbed Second-Order Multiagent Systems

Abstract

In this article, the distributed finite-time optimization problem is investigated for second-order multiagent systems with disturbances. To solve this problem, a feedforward-feedback composite control framework is established, which contains two main stages. In the first stage, for disturbed second-order individual systems with generally strongly convex cost functions, a composite finite-time optimization control scheme is proposed based on the combination of adding a power integrator and the finite-time disturbance observer techniques and the use of the cost functions' gradients and Hessian matrices. In the second stage, based on the result of the first stage, a distributed composite finite-time optimization control framework is built for disturbed second-order multiagent systems with quadratic-like local cost functions. This framework involves a kind of finite-time consensus algorithm, some novel distributed finite-time estimators designed for each agent to estimate the velocity, the gradient and Hessian matrix for the local cost function of any other agent, and some optimization terms in the form of the optimization controllers proposed in the first stage and based on the estimates from the distributed estimators. The finite-time convergence of the closed-loop systems is rigorously proved. The simulation results illustrate the effectiveness of the proposed control framework.